Question

A ball falling freely in the field of gravity passed the final section of its trajectory of length 45 m during time interval 1 sec. Find the
height from which the ball fell if its initial velocity was zero. Give your answer in meters m]. Assume the free fall acceleration to be
10 m/s2. The air resistance is negligible.

Answer 1

The distance trevelled by the free falling ball is:

$$d_{last} = v_0t + \dfrac{gt_{last}^2}{2}$$

where $v_0$ is the initial speed of ball at the beginning of the last section, $g = 10m/s^2$ is the free fall acceleration, $t_{last} = 1s$ is the time of covering the last section, $d_{last}= 45m$ is the length of the last section.

Expressing $v_0$, obtain:

$$v_0 = d_{last} - \dfrac{gt_{last}^2}{2} = 45-\dfrac{10\cdot 1^2}{2} = 40m/s$$

In order to gain such velocity from the rest, the ball should have spent the following amount of time:

$$t = \dfrac{v_0}{g} = \dfrac{40}{10} = 4s$$

In this time it covered the following distance:

$$d = \dfrac{gt^2}{2} = \dfrac{10\cdot 4^2}{2} = 80m$$

Thus, the total height from which the ball fell is:

$$h = d + d_{last} = 80m + 45m = 125m$$

Answer. 125 m.