A stone thrown vertically upwards reached its maximum height in 2 seconds. the modulus of its initial velocity

A stone thrown vertically upwards reached its maximum height in 2 seconds. the modulus of its initial velocity 1) cannot be calculated on the basis of only these data 2) is equal to zero 3) is approximately equal to 20 m / s 4) is approximately equal to 5 m / s

t = 2 s.

g = 10 m / s2.

V0 -?

When the stone moves, only the gravity force m * g, directed vertically downward, acts. Therefore, it will decelerate with the acceleration of gravity g until it comes to a complete stop. At the moment of stopping, the body will be at its maximum height.

The height of the rise of the stone h will be expressed by the formula: h = (V0 ^ 2 – V2) / 2 * g, h = V0 * t – g * t ^ 2/2.

hmax = V0 ^ 2/2 * g.

hmax = V0 * t – g * t ^ 2/2.

V0 ^ 2/2 * g = V0 * t – g * t ^ 2/2.

V0 ^ 2/2 * g – V0 * t + g * t ^ 2/2 = 0.

V0 ^ 2 – V0 * t * 2 * g + 2 * g * g * t ^ 2/2 = 0.

V0 ^ 2 – V0 * 2 * 2 * 10 + 2 * 10 * 10 * (2) ^ 2/2 = 0.

V0 ^ 2 – 40 * V0 + 400 = 0.

Let’s solve the quadratic equation according to Vieta’s theorem V0 = 20 m / s.

Answer: the stone was thrown at a speed of V0 = 20 m / s.