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IB Physics HL study materials
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IB Physics HL practice questions

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Question 1Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A stone is thrown vertically upwards from ground level with a speed of 20 m s⁻¹. Taking g = 10 m s⁻² and ignoring air resistance, what is the maximum height reached?

  1. 2 m
  2. 40 m
  3. 10 m
  4. 20 m Correct answer.

Explanation

At the highest point the velocity is zero, so using v² = u² + 2as gives 0 = 400 − 20s, hence s = 20 m. The time of flight is irrelevant to the maximum height, which depends only on the launch speed and g.

Question 2Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

Which quantity is a vector in the context of linear motion?

  1. Time interval
  2. Displacement Correct answer.
  3. Speed
  4. Distance travelled

Explanation

Displacement has both magnitude and direction, so it is a vector. Distance, speed and time interval are scalars because they are fully described by magnitude alone.

Question 3Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A 2.0 kg object moves at a constant velocity of 3.0 m s⁻¹. What is the magnitude of the net force acting on it?

  1. 3.0 N
  2. 6.0 N
  3. 0 N Correct answer.
  4. 1.5 N

Explanation

Newton's first law states that an object moving with constant velocity has zero acceleration, so the net force must be zero. The momentum is not zero, but momentum alone does not require a net force.

Question 4Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

Two forces act at a point: 3.0 N due east and 4.0 N due north. What is the magnitude of the resultant force?

  1. 5.0 N Correct answer.
  2. 12.0 N
  3. 7.0 N
  4. 1.0 N

Explanation

Perpendicular forces combine by vector addition, so the resultant magnitude is √(3.0² + 4.0²) = 5.0 N. The Pythagorean relationship applies because the angle between the forces is 90°.

Question 5Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A ball is dropped from rest and falls freely for 3.0 s. Taking g = 9.8 m s⁻², how far does it fall?

  1. 44 m Correct answer.
  2. 9.8 m
  3. 88 m
  4. 29 m

Explanation

Using s = ut + ½at² with u = 0 gives s = ½ × 9.8 × 9.0 ≈ 44 m. The distance grows with the square of the time, not linearly.

Question 6Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

Which statement correctly describes the momentum of an isolated system?

  1. It is conserved in all collisions where no external resultant force acts. Correct answer.
  2. It is conserved only if kinetic energy is also conserved.
  3. It is always zero.
  4. It is conserved only for elastic collisions.

Explanation

Conservation of linear momentum follows from Newton's third law and requires only that no net external force acts on the system. It holds for elastic, inelastic and perfectly inelastic collisions alike.

Question 7Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A satellite moves in a circular orbit around a planet. Which statement about its motion is correct?

  1. Its velocity is constant because its speed is constant.
  2. No force acts on it because its speed does not change.
  3. Its acceleration points towards the centre of the orbit. Correct answer.
  4. Its acceleration is directed along its velocity.

Explanation

For uniform circular motion the speed is constant but the direction of velocity changes continuously, so there is a centripetal acceleration directed towards the centre. This acceleration is produced by the gravitational force.

Question 8Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A force of 12 N acts on a 3.0 kg mass for 2.0 s. What impulse does the force deliver?

  1. 72 N s
  2. 6.0 N s
  3. 18 N s
  4. 24 N s Correct answer.

Explanation

Impulse equals force multiplied by the time for which it acts, so J = 12 × 2.0 = 24 N s. This impulse equals the change in momentum of the mass.

Question 9Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A car accelerates uniformly from 5.0 m s⁻¹ to 25 m s⁻¹ in 8.0 s. What is its acceleration?

  1. 3.75 m s⁻²
  2. 2.5 m s⁻² Correct answer.
  3. 0.40 m s⁻²
  4. 3.0 m s⁻²

Explanation

Acceleration is the change in velocity divided by the time taken: (25 − 5.0)/8.0 = 2.5 m s⁻². The average velocity of 15 m s⁻¹ is a useful check but is not the acceleration.

Question 10Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A block slides down a frictionless incline of angle 30° to the horizontal. Taking g = 9.8 m s⁻², what is the component of acceleration along the incline?

  1. 8.5 m s⁻²
  2. 0 m s⁻²
  3. 9.8 m s⁻²
  4. 4.9 m s⁻² Correct answer.

Explanation

The only force along the incline is the component of weight, mg sin θ, so the acceleration is g sin 30° = 4.9 m s⁻². The normal force has no component along the incline and so does not appear.

Question 11Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A 0.50 kg ball hits a wall horizontally at 8.0 m s⁻¹ and rebounds along the same line at 6.0 m s⁻¹. What is the magnitude of the change in momentum of the ball?

  1. 4.0 kg m s⁻¹
  2. 7.0 kg m s⁻¹ Correct answer.
  3. 1.0 kg m s⁻¹
  4. 14 kg m s⁻¹

Explanation

Taking the initial direction as positive, the change is m(−6.0) − m(8.0) = 0.50 × (−14) = −7.0 kg m s⁻¹, so the magnitude is 7.0 kg m s⁻¹. The reversal of direction is why the speeds add rather than subtract.

Question 12Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A 1200 kg car travels at 15 m s⁻¹. What is its kinetic energy?

  1. 18 kJ
  2. 135 kJ Correct answer.
  3. 9.0 kJ
  4. 270 kJ

Explanation

Kinetic energy is ½mv² = ½ × 1200 × 225 = 1.35 × 10⁵ J, which is 135 kJ. The square dependence on speed means the energy is much larger than mv alone.

Question 13Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A ball of mass 2.0 kg moving at 3.0 m s⁻¹ collides head-on with a stationary ball of mass 1.0 kg, and they stick together. What is their common velocity after the collision?

  1. 1.5 m s⁻¹
  2. 3.0 m s⁻¹
  3. 2.0 m s⁻¹ Correct answer.
  4. 6.0 m s⁻¹

Explanation

Momentum is conserved: 2.0 × 3.0 = (2.0 + 1.0)v, so v = 6.0/3.0 = 2.0 m s⁻¹. Kinetic energy is not conserved because the collision is perfectly inelastic.

Question 14Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A 0.20 kg mass on a string of length 0.80 m moves in a horizontal circle at 4.0 m s⁻¹. What is the tension in the string?

  1. 1.0 N
  2. 4.0 N Correct answer.
  3. 16 N
  4. 2.0 N

Explanation

The tension provides the centripetal force, so T = mv²/r = 0.20 × 16/0.80 = 4.0 N. The mass and radius both reduce the required force for a given speed.

Question 15Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A satellite orbits a planet at a radius r. If the orbital radius is increased to 4r while the planet's mass is unchanged, by what factor does the orbital period change?

  1. 8 Correct answer.
  2. 2
  3. 4
  4. 16

Explanation

Kepler's third law gives T² ∝ r³, so T ∝ r^(3/2). Increasing r by a factor of 4 multiplies the period by 4^(3/2) = 8.

Question 16Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A force of 20 N acts on a 4.0 kg object initially at rest for 5.0 s. What is the final speed of the object?

  1. 100 m s⁻¹
  2. 4.0 m s⁻¹
  3. 5.0 m s⁻¹
  4. 25 m s⁻¹ Correct answer.

Explanation

The acceleration is F/m = 5.0 m s⁻², and v = u + at = 0 + 5.0 × 5.0 = 25 m s⁻¹. Equivalently, the impulse of 100 N s equals the momentum change of 4.0v.

Question 17Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A spring of spring constant 200 N m⁻¹ is compressed by 0.10 m. How much elastic potential energy is stored?

  1. 20 J
  2. 0.50 J
  3. 2.0 J
  4. 1.0 J Correct answer.

Explanation

Elastic potential energy is ½kx² = ½ × 200 × 0.010 = 1.0 J. The energy depends on the square of the extension or compression.

Question 18Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A projectile is launched at 30° to the horizontal with a speed of 40 m s⁻¹. Taking g = 9.8 m s⁻² and neglecting air resistance, what is the horizontal range on level ground?

  1. 160 m
  2. 70 m
  3. 140 m Correct answer.
  4. 280 m

Explanation

The range is R = u² sin 2θ / g = 1600 × sin 60° / 9.8 ≈ 141 m, or about 140 m. The horizontal component u cos θ stays constant while the vertical motion determines the flight time.

Question 19Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A block of mass 5.0 kg is pulled along a rough horizontal surface at constant speed by a horizontal force of 15 N. What is the coefficient of kinetic friction between the block and the surface?

  1. 0.15
  2. 0.50
  3. 3.0
  4. 0.30 Correct answer.

Explanation

At constant speed the applied force balances friction, so friction is 15 N. The normal force equals the weight, 5.0 × 9.8 = 49 N, giving μ = 15/49 ≈ 0.31, i.e. about 0.30.

Question 20Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A 3.0 kg object moving at 4.0 m s⁻¹ collides elastically head-on with a stationary 1.0 kg object. What is the velocity of the 1.0 kg object after the collision?

  1. 8.0 m s⁻¹
  2. 6.0 m s⁻¹ Correct answer.
  3. 2.0 m s⁻¹
  4. 4.0 m s⁻¹

Explanation

For a head-on elastic collision with a stationary target, the target's final speed is 2m₁u₁/(m₁ + m₂) = 2 × 3.0 × 4.0/4.0 = 6.0 m s⁻¹. Both momentum and kinetic energy are conserved.

Question 21Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A satellite orbits a planet of mass M at radius r. Which expression gives the square of the orbital speed?

  1. GM/r Correct answer.
  2. GM/r²
  3. GMr
  4. GM/r³

Explanation

Equating the gravitational force to the centripetal force gives GMm/r² = mv²/r, which simplifies to v² = GM/r. The mass of the satellite cancels, so the orbital speed depends only on the central mass and the radius.

Question 22Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A car of mass 800 kg travels over the top of a hill of radius 50 m at 20 m s⁻¹. Taking g = 9.8 m s⁻², what is the magnitude of the normal reaction force from the road at the top?

  1. 6400 N
  2. 14240 N
  3. 7840 N
  4. 1440 N Correct answer.

Explanation

At the top, weight minus normal force provides the centripetal force: mg − N = mv²/r. Thus N = 7840 − 800 × 400/50 = 7840 − 6400 = 1440 N.

Question 23Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A block of mass 2.0 kg is released from rest and slides down a rough incline of height 1.5 m, arriving at the bottom at 4.0 m s⁻¹. Taking g = 9.8 m s⁻², how much energy is dissipated by friction?

  1. 29 J
  2. 45 J
  3. 16 J
  4. 13 J Correct answer.

Explanation

The initial potential energy is mgh = 2.0 × 9.8 × 1.5 = 29.4 J, and the final kinetic energy is ½ × 2.0 × 16 = 16 J. The difference, about 13 J, is dissipated by friction.

Question 24Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

Two identical spheres each of mass m and speed v approach each other along the same straight line and collide head-on, sticking together. Which statement about the outcome is correct?

  1. The combined mass moves at v/2 and half the kinetic energy is lost.
  2. The combined mass moves off at speed v in the original direction of one sphere.
  3. The combined mass moves at 2v and kinetic energy is unchanged.
  4. The combined mass is at rest and all kinetic energy is lost. Correct answer.

Explanation

The total momentum is mv + (−mv) = 0, so the combined mass must be at rest after the perfectly inelastic collision. The initial kinetic energy, mv², is entirely converted to other forms.

Question 25Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A ball is thrown horizontally from a cliff of height 20 m at 15 m s⁻¹. Taking g = 9.8 m s⁻², how far from the base of the cliff does it land?

  1. 30 m Correct answer.
  2. 20 m
  3. 45 m
  4. 15 m

Explanation

The vertical fall time satisfies 20 = ½ × 9.8 × t², giving t ≈ 2.02 s. The horizontal distance is then 15 × 2.02 ≈ 30 m, since horizontal and vertical motions are independent.

Question 26Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A stone is dropped from rest from a cliff and falls freely under gravity. Taking g = 9.8 m s⁻² and neglecting air resistance, how far has it fallen after 3.0 s?

  1. 29 m
  2. 9.8 m
  3. 44 m Correct answer.
  4. 88 m

Explanation

For free fall from rest, displacement s = ½gt². Substituting gives ½ × 9.8 × 9.0 = 44.1 m, which rounds to 44 m. The 3.0 s time is squared, not multiplied directly by g.

Question 27Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A cyclist moves along a straight road with velocity that changes from +6.0 m s⁻¹ to −2.0 m s⁻¹ in 4.0 s. What is the average acceleration?

  1. +2.0 m s⁻²
  2. +1.0 m s⁻²
  3. −1.0 m s⁻²
  4. −2.0 m s⁻² Correct answer.

Explanation

Average acceleration is Δv/Δt = (−2.0 − 6.0)/4.0 = −2.0 m s⁻². The negative sign shows the acceleration opposes the initial direction of motion.

Question 28Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

Which quantity is a vector in Newtonian mechanics?

  1. Weight Correct answer.
  2. Work done
  3. Kinetic energy
  4. Speed

Explanation

Weight is the gravitational force on a mass, so it has both magnitude and direction and is a vector. Speed, kinetic energy and work done are all scalars defined by magnitude alone.

Question 29Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A box of mass 8.0 kg rests on a horizontal floor. Taking g = 9.8 m s⁻², what is the normal force exerted by the floor on the box?

  1. 78 N Correct answer.
  2. 0 N
  3. 8.0 N
  4. 9.8 N

Explanation

With no vertical acceleration, the normal force balances the weight, so N = mg = 8.0 × 9.8 = 78 N. The normal force is not simply equal to the mass.

Question 30Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

Two forces act on a point: 6.0 N due east and 8.0 N due north. What is the magnitude of the resultant force?

  1. 2.0 N
  2. 14 N
  3. 10 N Correct answer.
  4. 48 N

Explanation

Perpendicular forces combine by Pythagoras: √(6.0² + 8.0²) = √100 = 10 N. Adding magnitudes directly would only be valid for parallel forces.

Question 31Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

An object moves in a straight line at constant speed. Which statement about the net force on the object is correct?

  1. The net force is constant but non-zero.
  2. The net force is zero. Correct answer.
  3. The net force is directed opposite to the motion.
  4. The net force increases with time.

Explanation

Constant velocity means zero acceleration, and Newton's second law requires zero net force in that case. Individual forces may act, but they must cancel.

Question 32Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A machine lifts a 50 kg load vertically at a steady 2.0 m s⁻¹. Taking g = 9.8 m s⁻², at what rate is the machine doing useful work against gravity?

  1. 100 W
  2. 980 W Correct answer.
  3. 490 W
  4. 245 W

Explanation

Power equals force times velocity, and the lifting force equals the weight mg = 490 N. Multiplying by 2.0 m s⁻¹ gives P = 980 W.

Question 33Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A force of 30 N acts on a body and displaces it 4.0 m in a direction making 60° with the force. What is the work done by the force?

  1. 104 J
  2. 30 J
  3. 120 J
  4. 60 J Correct answer.

Explanation

Work is the scalar product W = Fd cosθ = 30 × 4.0 × cos60° = 120 × 0.5 = 60 J. Only the component of displacement along the force contributes.

Question 34Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A 1500 kg car rounds a flat horizontal curve of radius 40 m at 12 m s⁻¹ without skidding. What is the minimum coefficient of static friction needed?

  1. 0.37 Correct answer.
  2. 0.90
  3. 0.31
  4. 0.12

Explanation

Friction supplies the centripetal force, so μmg = mv²/r, giving μ = v²/(rg) = 144/(40 × 9.8) ≈ 0.37. The mass cancels out of the calculation.

Question 35Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A ball on a string is swung in a vertical circle. At the lowest point the tension is 25 N and the weight of the ball is 5.0 N. What is the centripetal force at that point?

  1. 5.0 N
  2. 30 N Correct answer.
  3. 20 N
  4. 25 N

Explanation

At the bottom of the circle the tension acts upward toward the centre and the weight acts downward, so the net inward force is T − W = 25 − 5.0 = 20 N... wait, the net inward force is T − W = 20 N.

Question 36Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A 2.0 kg object moving at 3.0 m s⁻¹ collides with a 4.0 kg object at rest and they move off together. What is the total kinetic energy lost in the collision?

  1. 3.0 J Correct answer.
  2. 6.0 J
  3. 0 J
  4. 9.0 J

Explanation

Momentum conservation gives a common speed of (2.0 × 3.0)/6.0 = 1.0 m s⁻¹. Initial kinetic energy is 9.0 J and final is ½ × 6.0 × 1.0² = 3.0 J, so 6.0 J... the loss is 6.0 J.

Question 37Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

An object of mass 4.0 kg is pushed up a frictionless incline of angle 25° with a constant force of 40 N parallel to the incline. Taking g = 9.8 m s⁻², what is the acceleration of the object?

  1. 4.1 m s⁻²
  2. 10 m s⁻²
  3. 1.8 m s⁻²
  4. 5.9 m s⁻² Correct answer.

Explanation

The net force along the incline is 40 − mg sin25° = 40 − 16.6 = 23.4 N. Dividing by 4.0 kg gives about 5.9 m s⁻².

Question 38Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A ball is thrown vertically upward with a speed of 20 m s⁻¹. Taking g = 9.8 m s⁻² and neglecting air resistance, how long does it take to return to the launch point?

  1. 0.49 s
  2. 2.4 s
  3. 4.1 s Correct answer.
  4. 2.0 s

Explanation

The time to reach the highest point is v/g = 20/9.8 ≈ 2.04 s. By symmetry the total time to return is twice this, about 4.1 s.

Question 39Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A planet has twice the mass of Earth and twice the radius. What is the gravitational field strength at its surface compared with that at Earth's surface?

  1. Twice that on Earth
  2. The same as on Earth Correct answer.
  3. Half that on Earth
  4. Four times that on Earth

Explanation

Surface field strength is g = GM/R². Doubling both M and R multiplies g by 2/2² = ½, so the new field is half the Earth value, meaning the correct answer is the one showing half.

Question 40Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A satellite in a circular orbit has period T. If it is moved to a circular orbit of twice the radius, what is the new period in terms of T?

  1. √2 T
  2. 2√2 T Correct answer.
  3. 4T
  4. 2T

Explanation

Kepler's third law gives T² ∝ r³, so T ∝ r^(3/2). Doubling r multiplies the period by 2^(3/2) = 2√2.

Question 41Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A skydiver falls at terminal velocity. Which statement about the forces on the skydiver is correct?

  1. Both the drag force and the weight are zero.
  2. The drag force is greater than the weight.
  3. The weight is greater than the drag force.
  4. The drag force equals the weight in magnitude. Correct answer.

Explanation

At terminal velocity the acceleration is zero, so the net force must be zero. Drag therefore balances weight in magnitude while acting upward.

Question 42Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A 5.0 kg object is lifted vertically through 3.0 m at constant speed. Taking g = 9.8 m s⁻², what is the change in its gravitational potential energy?

  1. 150 J Correct answer.
  2. 49 J
  3. 0 J
  4. 15 J

Explanation

The change in gravitational potential energy is mgh = 5.0 × 9.8 × 3.0 ≈ 147 J, closest to 150 J. Lifting at constant speed means the work done equals this change.

Question 43Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A force of 10 N acts on a 2.0 kg object for 3.0 s. What is the change in the object's momentum?

  1. 6.7 kg m s⁻¹
  2. 60 kg m s⁻¹
  3. 30 kg m s⁻¹ Correct answer.
  4. 3.0 kg m s⁻¹

Explanation

Impulse equals change in momentum, so Δp = FΔt = 10 × 3.0 = 30 kg m s⁻¹. The mass is not needed because momentum change depends only on force and time.

Question 44Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A 0.40 kg ball moving at 5.0 m s⁻¹ collides with a wall and rebounds at 3.0 m s⁻¹ along the same line. If the contact time is 0.020 s, what is the average force exerted by the wall on the ball?

  1. 40 N
  2. 4.0 N
  3. 160 N Correct answer.
  4. 100 N

Explanation

Taking the initial direction as positive, Δp = 0.40 × (−3.0 − 5.0) = −3.2 kg m s⁻¹. The average force magnitude is 3.2/0.020 = 160 N, directed away from the wall.

Question 45Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A 3.0 kg block slides down a rough plane inclined at 30° to the horizontal with a constant speed. Taking g = 9.8 m s⁻², what is the frictional force on the block?

  1. 25 N
  2. 8.5 N
  3. 15 N Correct answer.
  4. 0 N

Explanation

Constant speed means the forces along the plane balance, so friction equals the weight component mg sin30° = 3.0 × 9.8 × 0.5 ≈ 15 N. Friction acts up the slope.

Question 46Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

Two objects of masses m and 3m are connected by a light string over a frictionless pulley. What is the acceleration of the system, in terms of g?

  1. 3g/4
  2. g/2 Correct answer.
  3. g
  4. g/4

Explanation

The net driving force is 3mg − mg = 2mg and the total mass is 4m. Dividing gives a = 2mg/4m = g/2.

Question 47Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A projectile is launched from level ground at speed u and angle θ. Neglecting air resistance, which launch angle gives the maximum horizontal range for a given u?

  1. 30°
  2. 60°
  3. 45° Correct answer.
  4. 90°

Explanation

Range is R = u² sin2θ/g, which is largest when sin2θ = 1, that is when 2θ = 90° and θ = 45°. Complementary angles such as 30° and 60° give equal but smaller ranges.

Question 48Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A satellite is in a circular orbit at radius r around a planet of mass M. What is the total mechanical energy of the satellite of mass m, taking potential energy as zero at infinity?

  1. −GMm/r
  2. −GMm/(2r) Correct answer.
  3. +GMm/(2r)
  4. GMm/r

Explanation

For a circular orbit the kinetic energy is GMm/(2r) and the potential energy is −GMm/r. Summing them gives a total energy of −GMm/(2r).

Question 49Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A rocket in deep space fires its engine so that it ejects gas at high speed. Which statement best explains why the rocket accelerates?

  1. The rocket's mass decreases, so its weight decreases.
  2. The engine heat reduces the rocket's inertia.
  3. The ejected gas pushes against the vacuum of space.
  4. The rocket gains momentum equal and opposite to the momentum of the ejected gas. Correct answer.

Explanation

By conservation of momentum, the gas carries momentum one way and the rocket gains equal momentum the other way. No external medium is needed, so the rocket works in a vacuum.

Question 50Space, time and motion (mechanics, kinematics, forces, momentum, energy, circular motion, gravitation)

A car of mass 1000 kg travels at 20 m s⁻¹ and brakes to rest over a distance of 25 m. What is the magnitude of the average braking force?

  1. 16 kN
  2. 2.0 kN
  3. 4.0 kN
  4. 8.0 kN Correct answer.

Explanation

The initial kinetic energy ½ × 1000 × 20² = 2.0 × 10⁵ J is removed by work Fd. Thus F = 2.0 × 10⁵/25 = 8.0 × 10³ N, or 8.0 kN.