Question

A key falls from a bridge that is 45 m above the water. It falls directly into a model boat, moving with constant velocity, that is 12 m from the point of impact when the key is re- leased. What is the speed of the boat

Answer 1

Answer:

4m/s

Explanation:

The motion is in downward direction, and the boat is moving with constant velocity, the position of the boat horizontally is 12m before the key fall.

The height difference "h"= ( y- y°)= 45 m

We can determine the needed time the key requires to reach the water using the expression from Newton's law

h= v(o) + 1/2 at^2

g= acceleration due to gravity= 9.8m/s^2

h= v(o) + 1/2 gt^2 -------------------------eqn*)

V(o)= 0 for the key= initial velocity

h= height that the key falls= 45m

If we substitute the above values into eqn(*) we have

We can make t^2 subject of the formula since v(0)= 0

t^2= h/(1/2 g)

= 45/(1/2× 9.8)

t^2= 45/4.9=9.18

t= √9.18

t=3.03 secs

Since the boat was moving with constant velocity,

Then Velocity= distance/ time

= 12/3.03

Velocity= 4m/s

Hence, the speed of the boat is 4m/s