Review interactive solution 2.57 at before beginning this problem. a woman on a bridge 86.7 m high sees a raft floating at a constant speed on the river below. she drops a stone from rest in an attempt to hit the raft. the stone is released when the raft has 4.22 m more to travel before passing under the bridge. the stone hits the water 2.16 m in front of the raft. find the speed of the raft.

  The speed of the raft is 1.5 m / s

Explanation:

It is observed that this is a problem of free fall for the stone and uniform movement for the raft. Let's start by calculating the time it takes for the stone to reach the river.

      Y = Vo t - ½ g t²

As the stone is released the initial velocity is zero

     Y = - ½ g t²

      t = √ 2y / g

      t = √ 2 86.7 / 9.8

      t = 4.2 s

This is the time it takes for the stone to reach the water, they also tell us that the raft is at 4.22 at the start of the movement (release the stone) and at 2.16 m when the stone reached the river, therefore, the distance traveled by the raft in time is

      Xt = X1 + X2

      Xt = 4.22 +2.16

      Xt = 6.38 m

As the raft goes at constant speed

      V = Xt / t

      V = 6.38 / 4.2

      V = 1.5 m / s

   The speed of the raft is 1.5 m / s  

this could be newton#'s law of cooling. the cooling curve is exponential