5. A post is driven into the ground by means of a blow from a pile-driver. The pile-driver falls from rest from a height of 1.6 m above the top of the post.
- Show that the speed of the pile-driver just before it hits the post is \(5.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). (2 marks)
The post has mass 6 kg and the pile-driver has mass 78 kg . When the pile-driver hits the top of the post, it is assumed that the there is no rebound and that both then move together with the same speed.
- Find the speed of the pile-driver and the post immediately after the pile-driver has hit the post.
The post is brought to rest by the action of a resistive force from the ground acting for 0.06 s .
By modelling this force as constant throughout this time, - find the magnitude of the resistive force,
- find, to 2 significant figures, the distance travelled by the post and the pile-driver before they come to rest.
(4 marks)