5. (15 points) A massive vertical plate is fixed on a car moving at a speed of $4 \mathrm{M} / \mathrm{c}$. A ball is flying towards it at a speed of $5 \mathrm{M} / \mathrm{c}$ relative to the Earth. Determine the speed of the ball relative to the Earth after a perfectly elastic normal collision.
Answer: $13 \mathrm{M} / \mathrm{c}$

Solution. We will associate the reference frame with the slab. Relative to this reference frame, the ball is flying at a speed of $5 M / c+4 M / c=9 M / c$. After a perfectly elastic collision, the ball's speed relative to the slab is also $9 \mathrm{M} / \mathrm{c}$. Therefore, relative to the Earth, the ball's speed is $9 \mathrm{M} / \mathrm{c}+4 \mathrm{m} / \mathrm{c}=13 \mathrm{m} / \mathrm{c}$.