# Which Tennis Ball Lands Farther Away?

## Question:

Viola and Dakota each horizontally launch a tennis ball from the 6m tall railing of the second floor of their school for a lab. Viola launches her tennis ball with an initial horizontal velocity of 1.4 m/s and Dakota launches her tennis ball with an initial horizontal velocity of 2.1 m/s. Whose tennis ball lands farther away?

## Answer:

Final answer: Dakota's tennis ball will land farther away because it has a higher initial horizontal velocity (2.1 m/s) compared to Viola's ball (1.4 m/s), and the time to hit the ground is the same for both balls due to the same launch height and gravitational acceleration.

## Explanation:

**When Viola and Dakota launch their tennis balls horizontally from the 6m tall railing, we can use principles of projectile motion to determine whose tennis ball lands farther away.**

The horizontal distance (range) covered by a projectile launched horizontally from a certain height is given by the formula R = vx × t, where vx is the initial horizontal velocity, and t is the time taken to hit the ground. Time t can be determined using the formula for free fall t = √(2h/g), where h is the height from which the balls are dropped and g is the acceleration due to gravity.

Since the height and gravitational acceleration are constant for both tennis balls, the time t to hit the ground will be the same for both. Therefore, the tennis ball that covers the greater horizontal distance will be the one with the higher initial horizontal velocity. Since Dakota launches her tennis ball with an initial horizontal velocity of 2.1 m/s, greater than Viola's 1.4 m/s, Dakota's ball will land farther away.