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 4.5 m/s. The roof makes an angle of 27 Degree with the horizontal, and its lowest point is 14 m from the ground. (Ignore any effects due to air resistance.) How long after leaving the roof does the hammer hit the ground? What is the horizontal distance traveled by the hammer between the instant it leaves the roof and the instant it hits the ground?

Explanation / Answer

part a:

let vertically downward direction be considered positive.

initial vertical velocity=4.5*sin(27)=2.043 m/s

vertical distance=14 m

acceleration due to gravity=9.8 m/s^2

let time taken be t seconds.

then using the fromula:

displacement=initial velocity*time+0.5*acceleration*time^2

==>14=2.043*t+0.5*9.8*t^2

==>4.9*t^2+2.043*t-14=0

solving for t, we get t=1.4946 seconds

so it will hit the ground in 1.4946 seconds

b) horizontal distance travelled=horizontal speed*time

=4.5*cos(27)*1.4946=5.9926 m

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