We are standing at a distance d=15 m away from a house. The house wall is h=6 m high and the roof has an inclination angle β=30 ∘. We throw a stone with initial speed v0=20 m/s at an angle α= 35 ∘. The gravitational acceleration is g=10 m/s2. (See figure)

(a) At what horizontal distance from the house wall is the stone going to hit the roof - s in the figure-? (in meters)
b) What time does it take the stone to reach the roof? (in seconds)

Vo = 20m/s[35o]

Xo = 20*cos35 = 16.38 m/s.
Yo = 20*sin35 = 11.47 m/s.

a. Tr = (Y-Yo)/g = 0-11.47/-10=1.147 s = Rise time.

h = Yo*t + 0.5g*t^2 =
hmax = 11.47*1.147 - 5*1.147^2 = 6.58 m

h = 0.5g*t^2 = 6.58-6 = 0.58 m.
5t^2 = 0.58
t^2 = 0.116
Tf = 0.341 s. = Fall time.

Range=Xo*(Tr+Tf) = 16.38 * (1.147+0.341)= 24.4 m.

D = 24.4-15 = 9.4 m. From the wall.

b. T = Tr + Tf = 1.147 + 0.341 = 1.49 s.