One body was thrown vertically upwards from a height of 10 m. the other was released from a height of 20 m

One body was thrown vertically upwards from a height of 10 m. the other was released from a height of 20 m without initial speed. determine the initial velocity of the first body if the bodies fell to the ground at the same time.

Given:

H1 = 10 meters – the height from which the first body was thrown up;

H2 = 20 meters – the height from which the second body fell;

g = 10 m / s ^ 2 – free fall acceleration;

t1 = t2 – the time of falling to the ground of both bodies is the same.

It is required to find V0 (m / s) – the initial velocity of the first body.

Let’s find the time of the fall of the second body to the ground:

t2 = (2 * H2 / g) ^ 0.5 = (2 * 20/10) ^ 0.5 = (40/10) ^ 0.5 = 4 ^ 0.5 = 2 seconds.

Since, according to the condition of the problem, both bodies fell to the ground at the same time, it means that t1 is also equal to 2 seconds.

The equation of motion for the first body along the y-axis will look like this:

h = h1 + v0 * t – g * t ^ 2/2. At time t = 2 seconds, h will be 0 (since the body will reach the ground), then:

10 + v0 * 2 – 10 * 2 ^ 2/2 = 0;

10 + 2 * v0 – 20 = 0;

2 * v0 = 10;

v0 = 5 m / s.

Answer: the initial velocity of the first body is 5 m / s.