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/s2 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.