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 = 3.0 cm and h2 = 1.60 cm. With what speed must the ball be shot at point P for it to land at d = 3.5 cm?

hint:Did you treat the ball as a projectile as it flies through the air? Did you find the time of fall and then the required horizontal velocity as the start of the projectile motion? How much mechanical energy does it have just then? Did you include the potential energy and both types of kinetic energy? How does the mechanical energy there compare with the initial amount at point P?

Explanation / Answer

Final drop height = 3cm., or 0.003m.

Time to drop 0.003m = sqrt.(2h/g) = sqrt.(0.006/9.8) = 6.12*10^-4 sec.

Horizontal V to land 0.35m. from top = (0.035/ 6.12*10^-4 ) = 57.18m/sec.

KE leaving top = 1/2 (mv^2) = 1/2 (1 x 57.18^2) = 1634.77 Joules.

PE from start = (mgh) = (1 x 9.8 x (0.03 - 0.016)) =.1372 Joule.

(0.1372 + 1634.77) =1634.90 Joules total energy.

V required at P = sqrt.(2KE/m) = 1.765m/sec.

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