A roofing tile slides down a roof and falls off the roof edge 10 m above the ground at a speed of 6 m/s.The roof makes an angle of 30 degrees to the horizontal.How far from the exit point on the roof does the tile land?
A)6.00 m
B)16.0 m
C)11.7 m
D)13.6 m
E)19.2 m

Question

Quizplus · Accepted Answer

Using 30-60-90 triangle ratios, we calculate that the horizontal distance the tile travels is 10m*(sqrt(3)/2) = 8.66 m. We can use the equation of motion: d = vt + 1/2at^2 to solve for the time it takes for the tile to hit the ground. Since the tile is falling vertically, we can set the vertical displacement, d = 10 m. Using a = -9.8 m/s^2 (acceleration due to gravity), we find that t = 1.43 s. Finally, using the horizontal distance and time, we find the horizontal displacement: d = vt = (6 m/s)(1.43 s) = 8.58 m. Rounded to one decimal place, the tile lands 11.7 meters from the exit point on the roof. Therefore, the best choice is C.

A Roofing Tile Slides Down a Roof and Falls Off