To determine the velocity and acceleration of the ball at a given time, we need to consider the effect of gravity on its motion. Assuming negligible air resistance, we can use the following equations of motion:
For velocity: v = u + at
For displacement: s = ut + (1/2)at^2
For the given situation, the ball is thrown vertically upwards, so the initial velocity (u) is 15 m/s, and the acceleration due to gravity (a) is -9.8 m/s² (taking g = 9.8 m/s² as the approximate acceleration due to gravity).
Let's find the velocity and displacement of the ball after 2 seconds:
- Velocity (v): v = u + at v = 15 m/s + (-9.8 m/s²) × (2 s) v = 15 m/s - 19.6 m/s v = -4.6 m/s
The negative sign indicates that the velocity is directed downwards, as the ball is moving in the opposite direction to its initial upward motion.
- Displacement (s): s = ut + (1/2)at^2 s = (15 m/s) × (2 s) + (1/2) × (-9.8 m/s²) × (2 s)^2 s = 30 m - 19.6 m s = 10.4 m
The positive displacement indicates that the ball has reached a maximum height of 10.4 meters above its initial position.
Therefore, after 2 seconds, the velocity of the ball is -4.6 m/s (directed downward), and the displacement is 10.4 meters above its initial position.