A woman on a bridge 77.4 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 7.07 m more to travel before passing under the bridge. The stone hits the water 4.18 m in front of the raft. Calculate the speed of the raft.
The raft moves 11.25 m during the time it takes for the stone to hit the water. Compute that time (t) and then use it to compute the raft's velocity.
77.4 m = (g/2) t^2 leads to ->
t = 3.97 s
Take it from there
Sorry about the repeat post; computer problems here
To solve this problem, we will use the principles of kinematics and calculate the time it takes for the stone to hit the water, and then use this time to find the speed of the raft.
Let's break down the problem step by step:
1. Determine the time it takes for the stone to hit the water:
- The height of the bridge is given as 77.4 m.
- The stone is released when the raft has 7.07 m more to travel before passing under the bridge. This means the total distance the stone has to cover is (77.4 + 7.07) m.
- We can use the equation for vertical motion: h = (1/2) * g * t^2, where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time taken.
- Plugging in the values, we have: (77.4 + 7.07) = (1/2) * 9.8 * t^2
- Solve for t: t^2 = (2 * (77.4 + 7.07))/9.8 then take the square root to find t.
2. Calculate the distance traveled by the raft in time t:
- We know that the stone hits the water 4.18 m in front of the raft.
- The distance traveled by the raft in time t is given by the equation d = v * t, where d is the distance, v is the velocity (or speed), and t is the time.
- Rearranging the equation, we have v = d/t.
- Plugging in the values, we have: v = 4.18/t.
3. Calculate the speed of the raft:
- Substituting the value of t from step 1 into the equation from step 2, we have: v = 4.18/(sqrt((2 * (77.4 + 7.07))/9.8))
Using a calculator, you can now evaluate this expression to find the speed of the raft.