Question

a student throws a rock upwards. The rock reaches a maximum height 2.4 seconds after it was released. How fast was the rock thrown?

Answer 1

We can find the initial velocity of the rock from the kinematic equation:

$$v=v_0+gt,$$

here, $v=0\ \dfrac{m}{s}$ is the final velocity of the rock at the maximum height, $v_0$ is the initial velocity of the rock, $g=-9.8\ \dfrac{m}{s^2}$ is acceleration due to gravity and $t=2.4\ s$ is the time that the rock takes to reach the maximum height.

Then, from this equation we can calculate the initial velocity of the rock:

$$v_0=-gt=-(-9.8\ \dfrac{m}{s^2})\cdot 2.4\ s=23.52\ \dfrac{m}{s}.$$

Answer:

$v_0=23.52\ \dfrac{m}{s}.$