While playing a game of pool the cue ball slides off the table moving at 3.1 m/s

Question

While playing a game of pool the cue ball slides off the table moving at 3.1 m/s. If the ball leaves the table moving entirely horizontally and the table top is 0.94 meters above the floor, calculate the following: 2. a. The time the ball was in the air before hitting the floor b. How far the ball moved horizontally from the ledge of the table. c. The final velocity's x-component as well as the final velocity's y-component. d. The speed the ball strikes the ground with and what angle it strikes at.

Explanation / Answer

(A) ball leaves horizontally,

so initial vertical velocity, v0y = 0

yf - yi = v0y t + ay t^2 / 2

0 - 0.94 = 0 - 9.8 t^2 / 2

t = 0.438 sec  

(B) in horizontal, a = 0

x = v0x t

x = (3.1)(0.438) = 1.36 m

(C) vx = v0x = 3.1 m/s

vy = v0y +ay t= 0 - (9.8 x 0.438) = - 4.29 m/s

(D) v = sqrt(Vx^2 + vy^2) = 5.30 m/s

theta = tan^-1(vy/vx) = - 54 deg

or 54 deg below the horizontal.

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