# With what initial speed the body is thrown vertically upward if in 2

**With what initial speed the body is thrown vertically upward if in 2 seconds the speed of the body it has a speed of 5 m per second. what is the lifting height?**

Given:

v = 5 meters per second – the speed of a body thrown vertically upward after a time interval t;

t = 2 seconds – time interval;

g = 10 meters per second squared – the acceleration of gravity.

It is required to determine v0 (m / s) – the initial velocity of the body, as well as h (meter) – the height to which the body will rise.

Let’s find the initial speed of the body:

(v0 – v) / g = t;

v0 – v = g * t;

v0 = v + g * t = 5 + 2 * 10 = 5 + 20 = 25 m / s.

Find the total ascent time:

t1 = v0 / g = 25/10 = 2.5 seconds.

Then the lifting height will be equal to:

H = v0 * t1 – g * t12 / 2 = 25 * 2.5 – 10 * 2.52 / 2 =

= 62.5 – 31.25 = 31.25 meters.

Answer: the initial velocity of the body is 25 m / s, the height of the body’s rise will be 25 m / s.