The ball was thrown vertically upward twice. The second time he was told a speed 3 times faster than the first time.

The ball was thrown vertically upward twice. The second time he was told a speed 3 times faster than the first time. How many times higher does the ball rise on the second throw?

Without taking into account the air resistance, only the force of gravity acts on the ball in flight. The movement of the ball up to the highest point of the trajectory is uniformly slowed down, with an acceleration g = 9.8 m / s2 directed vertically downward.

In the first case, the time of lifting the ball:

t1 = V1 / g,

in the second case:

t2 = V ^ 2 / g = 3 V1 / g = 3 t1.

The lifting height of the ball in the first case: H1 = g t1 ^ 2,

and in the second: H2 = g t2 ^ 2.

Thus,

H2 / H1 = (t2 / t1) ^ 2 = 3 ^ 2 = 9.

Answer: 9 times higher.