A woman on a bridge 91.1 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 8.20 m more to travel before passing under the bridge. The stone hits the water 3.49 m in front of the raft. Find the speed of the raft.

Question

A woman on a bridge 91.1 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 8.20 m more to travel before passing under the bridge. The stone hits the water 3.49 m in front of the raft. Find the speed of the raft.

Answer 1

find the time to fall 92.1 meters.

How far did the raft travel (8.2-3.49)
speed=distance/time

Answer 2

To find the speed of the raft, we need to analyze the motion of the stone and the raft and find the time it takes for the stone to hit the water.

Let's set up a coordinate system where the positive y-axis points upward. The bridge is at a height of 91.1 m above the river, so the initial position of the stone is y = 91.1 m.

When the stone hits the water, its final position is y = 0 m. We can use kinematic equations to find the time it takes for the stone to reach this position.

The initial velocity of the stone is 0 m/s because it is released from rest. The acceleration due to gravity is -9.8 m/s² because it acts downward. The displacement in the y-direction is -91.1 m (from 91.1 m to 0 m).

Using the kinematic equation:

y = y0 + v0*t + (1/2)*a*t²

where y is the final position, y0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is the time, we can solve for t:

0 m = 91.1 m + 0 m/s * t + (1/2)(-9.8 m/s²) * t²

Rearranging the equation, we get:

-4.9 m/s² * t² = 91.1 m

t² = -91.1 m / -4.9 m/s²

t² ≈ 18.63 s²

Taking the square root of both sides, we find:

t ≈ √(18.63 s²)

t ≈ 4.32 s

Therefore, the time it takes for the stone to hit the water is approximately 4.32 seconds.

Now, let's find the distance the raft travels during this time.

The difference in the distances traveled by the stone and the raft is 3.49 m. This means that in 4.32 seconds, the raft moves 8.20 m + 3.49 m = 11.69 m.

Since speed is defined as distance divided by time, we can calculate the speed of the raft:

Speed = Distance / Time

Speed ≈ 11.69 m / 4.32 s

Speed ≈ 2.71 m/s

Therefore, the speed of the raft is approximately 2.71 m/s.