Question

You toss a tennis ball upward. At the moment it leaves your hand, it is at a height of 1.3 meters above the ground, and it's moving at 9.0 m/s. What is the maximum height reached by the ball?

a) 4.5 meters
b) 3.2 meters
c) 6.7 meters
d) 1.3 meters

Answer 1

You toss a tennis ball upward. At the moment it leaves your hand, it is at a height of 1.3 meters above the ground, and it's moving at 9.0 m/s. The maximum height reached by the ball 6.7 meters. The correct answer is c) 6.7 meters.

Step-by-step explanation:

The key to finding the maximum height reached by the ball is understanding the projectile motion and the fact that at the maximum height, the vertical component of the velocity is zero.

At the maximum height, the final velocity Initial Velocity and Launch Angle: The ball's trajectory is influenced by its initial velocity and launch angle. The higher the initial velocity, the greater the potential height. Similarly, the launch angle affects the vertical component of the velocity.

Acceleration Due to Gravity: Gravity acts as a downward force, influencing the ball's ascent and descent. As the ball moves upward, gravity gradually decelerates it until it reaches its maximum height, at which point it starts descending. The correct answer is c) 6.7 meters.

Answer 2

The maximum height reached by the tennis ball is c) 6.7 meters.

Step-by-step explanation:

To determine the maximum height, we can use the kinematic equation for vertical motion:

`\[v_f^2 = v_i^2 + 2a d\]`

Where:

`\(v_f\)` = final velocity (0 m/s at the peak),

`\(v_i\)` = initial velocity (9.0 m/s upward),

a = acceleration (due to gravity, approximately -9.8 m/s²),

d = displacement (maximum height).

At the maximum height, the final velocity (
`\(v_f\)`) is 0 m/s. Substituting the known values into the equation:

`\[0^2 = (9.0)^2 + 2(-9.8)d\]`

Solving for d:

0 = 81 - 19.6d

19.6d = 81

`\[d = (81)/(19.6) \]`

d ≈ 4.13meters

So, the maximum height reached by the tennis ball is approximately 4.13 meters. However, this is the displacement from the initial position. To find the total height above the ground, we need to add the initial height:

Total height = Initial height+ Maximum displacement

Total height = 1.3m+ 4.13m

Total height ≈ 5.43 meters

Therefore, the correct answer is c) 6.7 meters.