During a do-it-yourself roof repair project, you are on the roof of your house a

Question

During a do-it-yourself roof repair project, you are on the roof of your house and accidentally drop your hammer. The hammer then slides down the roof at constant speed of 3.7 m/s. The roof makes an angle of 31° with the horizontal, and its lowest point is 10 m from the ground. (Ignore any effects due to air resistance.)

(a) How long after leaving the roof does the hammer hit the ground?
in seconds
(b) What is the horizontal distance traveled by the hammer between the instant it leaves the roof and the instant it hits the ground?
in meters

Explanation / Answer

given,

speed = 3.7 m/s

angle = 31 degree

hammer's vertical speed = 3.7 * sin(31)

hammer's vertical speed = 1.905 m/s

by second equation of motion

s = ut + 0.5 * at^2

10 = 1.905 * t + 0.5 * 9.8 * t^2

t = 1.247 sec

after leaving the roof hammer hit the ground after 1.247 sec

horizontal velocity = 2.7 * cos(31)

horizontal distance travelled = horizontal speed * time

horizontal distance travelled = 2.7 * cos(31) * 1.247

horizontal distance traveled by the hammer = 2.886 m

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