A schoolboy in a physical education class threw a grenade at an angle of 45 °

A schoolboy in a physical education class threw a grenade at an angle of 45 ° to the horizon at a distance of 55 m. Determinant of the initial velocity and the time of its fall. 

∠α = 45 °.

L = 55 m.

g = 9.8 m / s2.

V0 -?

t -?

The movement of a grenade can be divided into two types: horizontally, it moves uniformly with a speed V0, vertically uniformly accelerated with an acceleration of gravity g.

The flight range L is expressed by the formula: L = V0 * cosα * t, where V0 is the speed of the grenade throw, t is the flight time of the grenade.

g = V0 * sinα / t1, where t1 is the time for the grenade to rise to the maximum height.

t1 = V0 * sinα / g.

t = 2 * t1 = 2 * V0 * sinα / g.

L = V0 * cosα * 2 * V0 * sinα / g = V0 ^ 2 * sin2α / g.

V0 ^ 2 = L * g / sin2α.

V0 = √ (L * g / sin2α).

V0 = √ (55 m * 9.8 m / s2 / sin2 * 45 °) = 23.2 m / s.

t = 2 * V0 * sinα / g.

t = 2 * 23.2 m / s * sin45 ° / 9.8 m / s2 = 3.35 s.

Answer: the throwing speed of the grenade is V0 = 23.2 m / s, the flight time of the grenade is t = 3.35 s.