A woman on a bridge 81.6 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 9.13 m more to travel before passing under the bridge. The stone hits the water 4.30 m in front of the raft. Find the speed of the raft.

Question

A woman on a bridge 81.6 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 9.13 m more to travel before passing under the bridge. The stone hits the water 4.30 m in front of the raft. Find the speed of the raft.

Answer 1

h = 0.5g*t^2 = 81.6 m.

4.9t^2 = 81.6
t^2 = 16.65
t = 4.08 s. to hit ground.

d = 9.13-4.30 = 4.83 m. = Distance the boat traveled in 4.08 s.

Speed = d/t = 4.83/4.08 = 1.18 m/s.

Answer 2

To find the speed of the raft, we need to calculate the time it takes for the stone to fall and compare it with the time it takes for the raft to cover the distance.

1. Firstly, let's calculate the time it takes for the stone to fall. We can use the equation for free fall:
h = (1/2) * g * t^2
where h is the vertical distance, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.

In this case, the stone falls 81.6 m. Plugging in the values:
81.6 = (1/2) * 9.8 * t^2

Simplifying the equation:
163.2 = 4.9 * t^2

Solving for t:
t^2 = 163.2 / 4.9
t^2 = 33.3
t ≈ √33.3
t ≈ 5.77 seconds

2. Now, let's calculate the time it takes for the raft to cover the distance. We can use the equation:
d = v * t
where d is the distance, v is the velocity (raft's speed), and t is the time.

The raft travels 9.13 m in distance. Plugging in the values:
9.13 = v * t

3. Since we know the stone hits the water 4.30 m in front of the raft, we can use this information to determine the time it takes for the raft to cover that additional distance.
The raft travels 4.30 m in distance. Plugging in the values:
4.30 = v * (t + Δt)
where Δt is the additional time.

Since we have the equation 9.13 = v * t from step 2, we can substitute it into the equation:
4.30 = v * (t + 9.13 / v)

4. Now, we have two equations with two variables:
9.13 = v * t (from step 2)
4.30 = v * (t + 9.13 / v) (from step 3)

We can solve these equations simultaneously to find the value of v (raft's speed).

5. Plugging in the value of t we found in step 1, we have:
4.30 = v * (5.77 + 9.13 / v)

Expanding the equation:
4.30 = 5.77v + 9.13

Rearranging the equation:
5.77v = 4.30 - 9.13
5.77v = -4.83

Dividing both sides by 5.77:
v = -4.83 / 5.77
v ≈ -0.837 m/s

Since the velocity cannot be negative in this context, we discard the negative sign:
v ≈ 0.837 m/s

Therefore, the speed of the raft is approximately 0.837 m/s.