Question

A rock is thrown straight upwards from the top of the tower/ At the instant when the rock is released from the thrower's hand, the rock is 25m above the ground and moving straight upwards. Just before the rock crashes into the mud, it is moving straight downwards at 24.3 m/s. Assume air resistance is negligible. After the rock reached the muddy ground, the rock continued to move downwards, embedding itself .2m deep in the muddy ground before coming to final rest. Assume that while moving .2m down into the mud, the rock slowed down at an approximately steady rate. Please show steps

a. Find the magnitude and direction of the rock's acceleration while it slowed down and came to rest in the mud.

b. How much time has passed as the rock, in contact with the mud, slowed down and came to rest?

Answer 1

Just before hitting the mud the velocity of the stone is 24.3 m/s

Now the stone enters the mud it feels a force and eventually stops. So the mud gives a backward force which is opposite to the velocity of the stone. So the acceleration is upward.

Now before stopping it moves a distance of 0.2 m

So from,

Where and is the initial and final vlocity. Final velocity is zero.

  

Now suppose the time passed is t sec.

So from,

  

This is the time.