A stone thrown horizontally from the roof of a house at a speed of 15 m / s fell to the ground at an angle of 60

A stone thrown horizontally from the roof of a house at a speed of 15 m / s fell to the ground at an angle of 60 to the horizon. What is the height of the roof of the house?

V0 = 15 m / s.

∠α = 60 °.

g = 10 m / s2.

h -?

Since only gravity, directed vertically downward, acts on the stone during movement, the movement of the stone can be divided into two types: horizontally, it moves uniformly with a speed Vx = V0, vertically uniformly accelerated, with gravitational acceleration g and an initial vertical speed Vо = 0.

At the moment of impact on the ground, the stone will have a horizontal component of velocity Vх and vertical Vу, which are mutually perpendicular.

Therefore, the speed of the stone at the moment of impact V will be the hypotenuse of a right-angled triangle with legs Vх and Vу, directed at an angle ∠α = 60 ° to the horizontal component of the velocity Vх.

tgα = Vх / Vу = V0 / Vу.

Vу = V0 / tgα.

Vу = 15 m / s / tg60 ° = 8.8 m / s.

h = (Vy2 – V0y2) / 2 * g = Vy2 / 2 * g.

h = (8.8 m / s) 2/2 * 10 m / s2 = 3.9 m.

Answer: the height of the roof of the house is h = 3.9 m.