Question

A woman on a bridge 90.0 m high sees a raft floating at

aconstant speed on the river below. She drops a stone fromrest in
an attempt to hit the raft. The stone is releasedwehn the raft has
6.00 m more to travel before passing under thebridge. The stone
hits the water 2.00 m in front of theraft. Find the speed of the
raft.

Answer 1

To find the speed of the raft, we can use the principle of conservation of energy. When the woman drops the stone, it starts with potential energy due to its height and then converts to kinetic energy as it falls.

Step-by-step explanation:

To find the speed of the raft, we can use the principle of conservation of energy. When the woman drops the stone, it starts with potential energy due to its height and then converts to kinetic energy as it falls. The kinetic energy of the stone when it hits the water is equal to the potential energy it had initially. We can use the equation:

mgh = 0.5mv^2

Where m is the mass of the stone, g is the acceleration due to gravity, h is the height of the bridge, and v is the speed of the stone when it hits the water. Rearranging the equation, we can solve for v:

v = √(2gh)

Substituting the given values h = 90.0 m and g = 9.8 m/s^2, we can calculate the speed of the stone when it hits the water. This speed is equal to the speed of the raft.

Answer 2

0.93 m/s

Step-by-step explanation:

t = Time taken

u = Initial velocity = 0

v = Final velocity

s = Displacement = 90 m

a = Acceleration = 9.81 m/s²

`s=ut+(1)/(2)at^2\\\Rightarrow 90=0* t+(1)/(2)* 9.81* t^2\\\Rightarrow t=\sqrt{(90* 2)/(9.81)}\\\Rightarrow t=4.3\ s`

So, the raft covered 6-2 = 4 m in 4.3 seconds

Speed = Distance / Time

`\text{Speed}=(4)/(4.3)=0.93\ m/s`

Speed of the raft is 0.93 m/s