Figure P10.54 shows a friend standing on the roof of a building that is \(51.8 \mathrm{~m}\) tall. The roof is square and measures \(20 \mathrm{~m}\) on a side. You want to shoot a paintball so that it lands on the roof and startles your friend, using a gun that shoots paintballs at a muzzle speed of \(42 \mathrm{~m} / \mathrm{s}\). The only problem is a slim billboard \(67.5 \mathrm{~m}\) high between you and the roof, \(20 \mathrm{~m}\) in front of the building. You position yourself in front of the billboard such that when you hold the gun \(1.5 \mathrm{~m}\) above the ground and fire, the paintball just barely gets over the billboard at the highest point in its trajectory.

(a) At what angle \(\theta\) above the horizontal do you need to shoot the ball to clear the billboard?

(b) What is your horizontal distance from the billboard?

(c) How long does the paintball take to move from the highest point in its trajectory to the height of the roof?

(d) Does the ball strike the roof?

(e) What is the speed of the ball when it strikes?

Data from Figure P10.54

Transcribed Image Text:

42 m/s not to scale billboard 67.5 m -20 m- -20 m 51.8 m