The body falls freely with no initial speed and hits the ground in 4 seconds. how long would the body fall

The body falls freely with no initial speed and hits the ground in 4 seconds. how long would the body fall to the ground if it was thrown down from the same height with an initial speed of 29.4 m / s.

Decision:

The path of a falling body, which began to fall from a state of rest, is found by the formula: S = g * t * t / 2. (1)

The path of a falling body, which began to fall at a certain initial speed, is found by the formula: S = v * t + g * t * t / 2. (2)

Here g = 9.8 m / s * s. Let’s find the path: S = 9.8 * 4 * 4/2 = 78.4 m.

By condition, expression (1) is equal to expression (2), therefore:

29.4 * t + 4.9 * t * t = 78.4, 4.9 * t * t + 29.4 * t – 78.4 = 0. The solution to this quadratic equation is available at the link

The second root does not fit, so t = 2 s.

Answer: the body would have fallen in 2 seconds.