Question

A tennis ball is hit with a vertical speed of 10 m/s and a horizontal speed of 30 m/s. How far will the ball travel horizontally before landing?
a. 10 m
b. 20 m
c. 40 m
d. 60 m
e. 80 m​

Answer 1

Answer:

D) 60 m

Explanation:

We can use the constant acceleration equation that contains displacement, initial velocity, acceleration, and time. We want to solve for the time that the ball was in the air first.

• Δx = v_i * t + 1/2at²  

Let's use this equation in terms of the y-direction.

• Δx_y = (v_i)y * t + 1/2a_y * t²

The vertical displacement will be 0 meters since the ball will be on the floor. The initial vertical velocity is 10 m/s, the vertical acceleration is g = 10 m/s², and we are going to solve for time t.

Let's set the upwards direction to be positive and the downwards direction to be negative. We must use -g to be consistent with our other values.

Plug the known values into the equation.

• 0 m = 10 m/s * t + 1/2(-10 m/s²) * t²

Simplify the equation.

• 0 = -10t + 5t²  
• 0 = 5t² - 10t

Factor the equation.

• 0 = 5t(t - 2)

Solve for t by setting both factors to 0.

• 5t = 0
• t - 2 = 0

We get t = 0, t = 2. We must use t = 2 seconds because it is the only value for t that makes sense in the problem.

Now that we have the time that the ball was in the air, we can use the same constant acceleration equation to determine the horizontal displacement of the tennis ball. We will use this equation in terms of the x-direction:

• Δx = v_i * t + 1/2at²
• Δx_x = (v_i)x * t + 1/2a_x * t²

Plug the known values into the equation.

• Δx_x = 30 m/s * 2 sec + 1/2(0 m/s²) * (2 sec)²

We can eliminate the right side of the equation since anything multiplied by 0 outputs 0.

• Δx_x = 30 * 2
• Δx_x = 60

The horizontal displacement of the ball is 60 meters. Therefore, the answer is D) 60 m.