In Figure 11-38, a small, solid, uniform ball is to be shot frompoint P so that

Question

In Figure 11-38, a small, solid, uniform ball is to be shot frompoint P so that it rolls smoothly along ahorizontal path, up along a ramp, and onto a plateau. Then itleaves the plateau horizontally to land on a game board, at ahorizontal distance d from the right edge of theplateau. The vertical heightsare h1 = 6.1cm andh2 = 2.1cm. With what speed must the ball be shot atpoint P for it to landat d = 9.3 cm?

Fig. 11-38
Problem 14.

I got two answers they both were wrong. First one 2.96m/s and1.03m/s. Please tell how to do this problem and the finalanswer.

Explanation / Answer

We are given information that:
h1 = 6.1cm = 0.061m , h2 = 2.1cm = 0.021m d = 9.30cm = 0.093m We converted units tometers.

We can apply conservation of energy at point P.
at the height h1 we have the following equation:
                                      (1/2)mU2 = mgh1+(1/2)mV2    U2 = 2gh1+ V2         If the ball is moving with the inital velocity V wehave this equation.

d = V(2h2/g)1/2             V = d /(2h2/g)1/2                 = 1.42 m/s                 
All you have to do is substitude the value of velocity in theequation we obtained with h1.
And we will get the value of V1
U2 = 2(9.81)(0.061) + (1.42)2 = 3.21
(3.21)1/2 = U = 1.79 m/s

You should check by yourself! hope this helps. :)
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