## Question

A stone is thrown vertically upwards with a velocity of 5.0 m/s. After time t, it reaches the original position. Neglecting air resistance, what is the time required for the ball to reach the highest position?

## Answer

By conservation of energy, the final velocity of the stone will be 5.0 m/s downwards. We also know that the acceleration of the stone is constant at 10m/s^{2} downwards. Hence, we can sketch a velocity-time graph.

The displacement upwards from 0 to 0.5 t must be equal to the displacement downwards from 0.5 t to t since the stone returns to its original position.

By symmetry, the highest point must be at 0.5 t.

Hence, the ball takes 0.5t to reach the highest point.