A woman on a bridge 90.0m 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 6.00m more to travel before passing under the bridge. The stone hits the water 2.00m in front of the raft. Find the speed of the raft.
I made a table with Y:-90m, A:9.8m/s^2, Vo: 0
So since y+ Vot+1/2at^2
90= 0+ ½(9.8) t^2
T+ 4.29
I figured the raft moves 4.00m.
So
4.00m/4.49s =.89 m/s
But the answer in the back of the book is .932m/s
What did I do wrong?
What you did wrong was forget that you had (correctly) calculated the time to reach the water as 4.29 s. You then changed it to 4.49 s.
The raft moves 4 m in the time it takes the stone to fall 90 m. That time T is given by the equation
(g/2)T^2 = 90
T = sqrt(180/g) = 4.29 s
V = 4/4.29 = 0.932 m/s
The problem is that you divided the distance traveled by the raft by ..4.49s.
I don't know where you got 4.49, but using the original time obtained by you with the time it takes for the rock to hit the water, would give you the answer in the book.
(time it takes for stone to hit water is same time traveled by raft)
thanks!
A woman on a bridge 75.0m 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 7.00m 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.
How did you get the time,?
2008 AND 2014? 😭
I apologize for the confusion. Here's how to solve the problem:
Let the speed of the raft be v, and the time it takes to reach the bridge be t.
Then we have two equations:
75 = (1/2)gt^2 (time it takes for the stone to hit the water)
v(t+4) = d + 7 (distance the raft travels in the same time it takes for the stone to hit the water is d+7, where d is the distance between the raft and the bridge when the stone is dropped)
We also know that the stone hits the water 4m in front of the raft, so:
d = 4 + vt
Substituting this into the second equation gives:
v(t+4) = 4 + vt + 7
Simplifying:
vt = 71
Substituting this into the first equation gives:
75 = (1/2)g(71/v)^2
Solving for v:
v = 3.41 m/s
Therefore, the speed of the raft is 3.41 m/s.