A player throws a ball upwards with an initial speed of 29.4 m s.
What is the direction of acceleration during the upward motion of the ball?
The direction of acceleration during the upward motion of the ball is vertically downward. This is because the acceleration due to gravity always acts downward towards the centre of the Earth, regardless of the direction of motion of the ball.
What are the velocity and acceleration of the ball at the highest point of its motion?
At the highest point of its motion: Velocity = 0 m s⁻¹ (the ball comes to rest momentarily before falling back). Acceleration = 9.8 m s⁻² acting vertically downward (acceleration due to gravity is always present).
Choose the m and s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of -axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion.
Taking downward direction as positive:
During upward motion: Position is negative (ball is above the highest point), Velocity is negative (moving upward, opposite to positive direction), Acceleration is positive (gravity acts downward).
During downward motion: Position is positive (ball is below the highest point), Velocity is positive (moving downward, same as positive direction), Acceleration is positive (gravity acts downward).
To what height does the ball rise and after how long does the ball return to the player’s hands? (Take m s and neglect air resistance).
Maximum height = 44.1 m, Total time to return = 6 s
Explanation
This question tests understanding of motion under gravity. The key concept is that acceleration due to gravity always acts downward with magnitude g = 9.8 m s⁻², irrespective of whether the body is moving up or down. At the highest point, velocity becomes zero momentarily but acceleration continues to act downward. For the numerical part, we use kinematic equations: v² = u² + 2as for height calculation, and v = u + at for time calculation.