Increase the Time of Flight of a Tennis Ball Launch

What combination of changes must produce an increase in time of flight of a second launch?

A machine launches a tennis ball at an angle of 25° above the horizontal at a speed of 14 meters per second. The ball returns to level ground.

A. decrease the launch angle and decrease the ball’s initial speed

B. decrease the launch angle and increase the ball’s initial speed

C. increase the launch angle and decrease the ball’s initial speed

D. increase the launch angle and increase the ball’s initial speed

Answer:

D. increase the launch angle and increase the ball’s initial speed

Explanation: For a body undergoing a projectile motion, the time of flight will be calculated using the formula t=(2usin∅)/g, where: - t = time of flight - u = the velocity a body undergoes during the motion - g = gravitational constant (9.81m/s^2) - ∅ = launch angle

Mathematically, as the velocity and angle of inclination increase, the time of flight also increases, provided that gravity is constant. Therefore, the correct combination to increase the time of flight of a second launch is to increase the launch angle and increase the ball’s initial speed.

How to increase the time of flight?

The angle at which the ball is released above the horizontal is known as the launch angle. By increasing the launch angle, the ball’s trajectory becomes more vertical, prolonging the duration of flight. This is because a higher launch angle results in a higher peak height, allowing the ball to spend more time in the air.

The ball’s initial speed, also known as its launch velocity, plays a crucial role in determining the time of flight. When the initial speed decreases, the ball’s horizontal velocity component also decreases. As a result, it takes the ball longer to cover a given horizontal distance, thereby extending its flight time.