A soccer ball is kicked horizontally at 16.1 m/s off the top of a field house and lands 37.5 metes from the base of the field house. Determine the height of the field house.
Time, t, to reach ground = Δx/vix
= 2.329 s
Use kinematics equation
Δy=viy*t+(1/2)g(t)²
= 10.92 m.
(g=-9.81 m/s²), viy=0)
To determine the height of the field house, we need to use the equation of motion to find the time it takes for the soccer ball to travel horizontally. Once we have the time, we can use it to calculate the vertical distance the ball falls, which will give us the height of the field house.
Let's break down the problem step by step:
Step 1: Calculate the time of flight
Since the soccer ball is kicked horizontally, we can use the formula:
Distance = Speed × Time
In this case, the horizontal distance traveled by the soccer ball is 37.5 meters, and the initial horizontal speed is 16.1 m/s. Therefore, we can rearrange the equation to solve for time:
Time = Distance / Speed
Time = 37.5 m / 16.1 m/s
Step 2: Calculate the height of the field house
The vertical distance traveled by the ball can be determined using the equation of motion:
Distance = 0.5 × Gravity × Time²
Since the ball is falling vertically, the initial vertical velocity is zero. We can ignore air resistance, so we use the acceleration due to gravity, which is approximately 9.8 m/s². Rearranging the equation, we have:
Distance = 0.5 × 9.8 m/s² × Time²
Now, substitute the calculated time from Step 1 into the equation:
Distance = 0.5 × 9.8 m/s² × (Time)²
Step 3: Calculate the height
Using the calculated distances, we can find the height of the field house. In this case, the vertical distance is the height we are looking for. Therefore:
Height = Distance
Height = 0.5 × 9.8 m/s² × (Time)²
Now, you can calculate the height of the field house using the equation and the values obtained in Step 1.