A trailer of mass 30000 kg moving at 20 m/s collides with a stationary train. They move together at 15 m/s for 15 s. Calculate the distance moved and the impulsive force.

$$
Distance = V \times t
$$
$$
Distance = 15 \text{ m/s} \times 15 \text{ s}
$$
$$
Distance = 225 \text{ m}
$$
The distance moved after the impact is $\boxed{225 \text{ m}}$.

• (iii) The impulsive force on the trailer on impact.

$$
F = \frac{-150000 \text{ kg m/s}}{0.5 \text{ s}}
$$
$$
F = -300000 \text{ N}
$$
The impulsive force on the trailer on impact is $\boxed{300000 \text{ N}}$ (magnitude).

16. d) Give a reason why when a passenger jumps from a floating boat, the boat moves backwards.
This occurs due to the conservation of momentum. As the passenger jumps forward, they exert a force on the boat in the backward direction. By Newton's Third Law, the boat exerts an equal and opposite force on the passenger, propelling them forward. The total momentum of the passenger-boat system remains zero (assuming it was initially at rest).

16. e) Give the reason why a safety seat belt used in a vehicle:

• i) Should have a wide surface area. A wide surface area distributes the force of impact over a larger area of the body, thereby reducing the pressure exerted on the body and minimizing injury.

• ii) Should be slightly extensible. Being slightly extensible allows the seat belt to stretch during an impact, which increases the time over which the stopping force acts. This increase in time reduces the magnitude of the force experienced by the occupant, thus reducing the risk of severe injury.

17. a) State Hooke's Law.
Hooke's Law states that the extension of a spring is directly proportional to the applied force, provided the elastic limit is not exceeded.