Problem 4-23 - Projectile - A

A girl throws a ball onto the roof of a house, as illustrated in the figure, and prepares to catch the ball with a baseball glove held \(1.0\; m\) above the ground. The ball rolls off the roof with a speed of \(3.2\; m/s.\)

Diagram of person throwing a ball on the roof and letting it roll down with dimensions indicated.
(a) From the time the ball left the roof, how long will it take to land in her glove?
(b) How far from the horizontal edge of the roof should she hold her glove?
(c) What is the ball's velocity as it reaches her glove?

Accumulated Solution

Diagram indicating all directions and angles.

Correct.

Diagram showing 4 possible coordinate systems A, B, C and D

Either A or B can be used but if we choose B then the acceleration will be positive. We will put the origin at the edge of the roof and the dispalcements will be positive as well.

As with all projectile problems we must solve the horizontal \((x)\) and vertical \((y)\) motions separately. We need the \(x\) and \(y\) components of the initial velocity.

They are:

Answer \(v_{o_x}\) \(v_{o_y}\)
(A)  \(v_0\cos33 = 2.68 \; m/s\) \(-v_0\sin33 = -1.74 \;m/s\)
(B) \(v_0\cos33 = 2.68 \;m/s\) \(v_0\sin33 = 1.74\; m/s\)
(C) \(v_0\sin33 = 1.74 \;m/s\) \(v_0\cos33 = 2.68\; m/s\)
(D) \(v_0\sin33 = 1.74\; m/s\) \(-v_0\cos33 = -2.68\; m/s\)