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.
The stone takes 4.08 sec to hit the water.
The boat moved 9.13-4.30=4.83m in 4.08s
So, its speed is 1.18 m/s
To find the speed of the raft, we need to consider the motion of both the stone and the raft.
Let's first calculate the time it takes for the stone to hit the water.
We know that the height of the bridge is 81.6 m and the stone hits the water 4.30 m in front of the raft. Therefore, the stone will take (81.6 + 4.30) m = 85.9 m to fall.
We can use the formula for the time it takes for an object to fall freely:
h = (1/2)gt^2
Where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Plugging in the values, we have:
85.9 = (1/2)(9.8)t^2
Simplifying the equation, we get:
17.18 = 4.9t^2
Dividing both sides of the equation by 4.9, we have:
t^2 = 3.5
Taking the square root of both sides, we find:
t = √3.5
t ≈ 1.87 seconds
Now, let's calculate the speed of the raft.
We know that the stone is released when the raft has 9.13 m more to travel before passing under the bridge. Therefore, the time it takes for the raft to cover this distance is the same as the time it takes for the stone to fall.
So, the speed of the raft can be calculated using the formula:
speed = distance / time
Plugging in the values, we have:
speed = 9.13 m / 1.87 s
speed ≈ 4.88 m/s
Therefore, the speed of the raft is approximately 4.88 m/s.