Question

An inflatable raft (unoccupied) floats down a river at an approximately constant speed of 4.8 m/s. A child on a bridge, 81 m above the river, sees the raft in the river below and attempts to drop a small stone onto the raft. The child releases the stone from rest. In order for the stone to hit the raft, what must be the horizontal distance between the raft and the bridge when the child releases the stone?

Answer 1

Answer:

19.5 m

Explanation:

t = Time taken

u = Initial velocity = 0 (Assumed thrown from rest)

s = Displacement = 81 m

g = Acceleration due to gravity = 9.81 m/s² = a

Equation of linear motion

$s=ut+\frac{1}{2}at^2\\\Rightarrow 81=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{81\times 2}{9.81}}\\\Rightarrow t=4.06371\ s$

The time taken for the stone to reach the river is 4.06371 seconds

Distance = Speed×Time

$Distance=4.8\times 4.06371=19.5\ m$

The horizontal distance between the raft and the bridge when the child releases the stone should be 19.5 m