A woman on a bridge 75.0m high sees a raft floating at a constant sped 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 7.00m more to travel before passing under the bridge. The stone hits the water 4.00m in front of the raft. Find the speed of the raft.

Question

A woman on a bridge 75.0m high sees a raft floating at a constant sped 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 7.00m more to travel before passing under the bridge. The stone hits the water 4.00m in front of the raft. Find the speed of the raft.

Answer 1

Use the same method described here:

http://www.jiskha.com/display.cgi?id=1230441164

The raft moves 3.0 m in the time it takes the stone to fall 75 m. Compute that time and do the division to get speed.

Answer 2

I didn't get how did she got 4.29s

Answer 3

YEAH! I got it already. THANKS!

Answer 4

Full steps

Answer 5

To find the speed of the raft, we need to analyze the motion of the stone and the raft.

Let's denote the speed of the raft as Vr and the time it takes for the raft to pass under the bridge as Tr.

The stone is dropped from rest, so its initial velocity is zero (V0 = 0). The only force acting on the stone is gravity, which causes it to accelerate downward at a rate of 9.8 m/s² (acceleration due to gravity).

Using the kinematic equation for vertical motion:

h = V0t + (1/2)gt²

where h is the height, V0 is the initial velocity, t is the time, and g is the acceleration due to gravity.

For the stone:

75.0m = 0t + (1/2)(9.8m/s²)t²
75.0m = 4.9m/s²t²

Simplifying the equation, we get:

15.3t² = 75.0m

Now, let's analyze the motion of the raft. The raft travels a distance of 7.00m less than the height of the bridge (75.0m - 7.00m = 68.0m) before the stone is released. Since the stone hits the water 4.00m in front of the raft, the total distance the raft travels is (68.0m + 4.00m = 72.0m).

Since the time it takes for the raft to pass under the bridge is Tr, and the speed of the raft is Vr, we can write the equation:

Tr = 72.0m / Vr

Now, we have two equations:

15.3t² = 75.0m (Equation 1)
Tr = 72.0m / Vr (Equation 2)

Since the stone hits the water 4.00m in front of the raft, the stone and the raft take the same amount of time to reach their respective points. So, t = Tr.

We can substitute Tr for t in Equation 1:

15.3(Tr)² = 75.0m

Rearranging the equation:

(Tr)² = 75.0m / 15.3

Taking the square root of both sides of the equation:

Tr = √(75.0m / 15.3)

Now, we can substitute Tr into Equation 2:

√(75.0m / 15.3) = 72.0m / Vr

Rearranging the equation:

Vr = (72.0m * 15.3) / √75.0m

Evaluating the expression:

Vr ≈ 7.66 m/s

Therefore, the speed of the raft is approximately 7.66 m/s.