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 4.3 m/s. The roof makes an angle of 29° with the horizontal, and its lowest point is 14 m from the ground. (Ignore any effects due to air resistance.)
(a) How long after leaving the roof does the hammer hit the ground?
s

(b) What is the horizontal distance traveled by the hammer between the instant it leaves the roof and the instant it hits the ground?
m

Explanation / Answer

The above situation is similar to the case of object thrown with velocity u at an angle below the horizontal from height h The equation of motion fro such an object in horizontal direction x = ucost in vertical direction y = usint + 0.5gt2 Where x is the horizontal distance travelled by the object             u is the initial speed = 4.3 m/s             t is the time spent by the object in air             y is the vertical distance travelled by the object = 14 m             g is the free fall acceleration = 9.8 m/s2 a) 14 m = (4.3 m/s)sin29*t + 0.5*9.8 m/s2*t2 a) 14 m = (4.3 m/s)sin29*t + 0.5*9.8 m/s2*t2 4.9t2 + 2.085t -14 = 0 t = 1.49 s b) x = (4.3 m/s)cos29*(1.49 s) x = 5.604 m b) x = (4.3 m/s)cos29*(1.49 s) x = 5.604 m

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