A stone is thrown horizontally from a great height with an initial velocity of 20 m / s.

A stone is thrown horizontally from a great height with an initial velocity of 20 m / s. In how many seconds will the velocity vector with the horizon make an angle of 60 degrees?

V0 = 20 m / s.

∠α = 60 °.

g = 10 m / s2.

t -?

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 at a speed Vx = V0, vertically uniformly accelerated, with gravitational acceleration g and an initial vertical speed Vо = 0.

The vertical component of the speed Vу will change according to the law: Vу = Vу + g * t = g * t.

t = Vу / g.

Therefore, the speed of the stone 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 = 20 m / s / tg60 ° = 11.8 m / s.

t = 11.8 m / s / 10 m / s2 = 1.18 s.

Answer: after t = 1.18 s the speed of the stone will be ∠α = 60 ° with the horizon.