In the figure here, a small, solid, uniform ball is to be shot from point P so t

Question

In the figure here, a small, solid, uniform ball is to be shot from point P so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance d from the right edge of the plateau. The vertical heights are h1 = 5.0 cm and h2 = 1.80 cm. With what speed must the ball be shot at point P for it to land at d = 7.5 cm?

http://edugen.wileyplus.com/edugen/courses/crs4957/art/qb/qu/c11/qu11_b.jpg

Explanation / Answer

The time for the ball to fall from h2 is h2 = 1/2*g*t^2 or t = sqrt(2*h2/g) = sqrt(2*0.0180/9.80) = 6.06x10^-2s So the velocity at the top of the plateau is v = d/t = 0.075/6.06x10^-2 = 1.24m/s Now use conservation of energy to find vP Let U (potential energy) at P = 0 So Kp = Ktop + Utop 1/2*m*vP^2 = 1/2*m*vTop^2 +m*g*h1 so vP = sqrt(vTop^2 + 2*g*h1) = sqrt(1.24^2 + 2*9.8*0.055) = 1.62m/s

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