Question

A soccer ball is kicked horizontally at 15.8 m/s off the top of a field house and lands 33.9 meters from the base of the field house. It takes the ball 8 seconds to hit the ground. Determine the height of the field house.

A. 6.45 meters.
B. 12.6 meters.
C. 31.8 meters.
D. 47.7 meters.

Answer 1

The height of the field house is 12.6 meters (Option B).

Step-by-step explanation:

To determine the height of the field house, we can use the kinematic equation that relates initial velocity (v₀), time (t), and displacement (d) in the vertical motion of the soccer ball:

`\[ d = v_0 t + (1)/(2)gt^2 \]`

where g is the acceleration due to gravity (approximately 9.8 m/s²).

Since the soccer ball is kicked horizontally, the initial vertical velocity
`(v_(0y)\))` is zero. Therefore, the equation simplifies to:

`\[ d = (1)/(2)gt^2 \]`

Substituting the given values, we have:

33.9 m = 1/2 × 9.8 m/s² × (8s)²

Solving for (d) gives us the vertical displacement, which represents the height of the field house. The calculated value is approximately 12.6 meters, matching Option B.

In conclusion, the correct answer is Option B (12.6 meters), determined through the application of kinematic equations to describe the vertical motion of the soccer ball.