Acceleration and Launch Velocity in a Football Game Scenario
What is the vertical component of the launch velocity when a kicker attempts a field goal in a football game at the UNT’s Apogee Stadium?
The vertical component of the launch velocity is approximately 14.30 m/s.
Calculation of the Vertical Component of the Launch Velocity:
Acceleration (a) = 55 m/s²
Time (t) = 0.13 s
Launch angle (θ) = 30°
To determine the vertical component of the launch velocity, we first calculate the change in velocity (Δv) in the vertical direction using the formula Δv = a × t. Substituting the values given:
Δv = 55 m/s² × 0.13 s = 7.15 m/s
Next, we use trigonometry to find the launch velocity's vertical component. The vertical component (v_y) can be calculated as v_y = v × sin(θ), where θ is the launch angle. Rearranging the equation:
v = v_y / sin(θ)
Substitute the value of Δv into the equation to find the vertical component of the launch velocity:
v = 7.15 m/s / sin(30°) ≈ 14.30 m/s
Therefore, the vertical component of the launch velocity is approximately 14.30 m/s. In this scenario, understanding the acceleration and time of contact with the kicker's foot allows us to calculate the change in velocity in the vertical direction. By applying trigonometric principles, we determine the vertical component of the launch velocity with the given launch angle. The accurate vertical component is crucial for analyzing the ball's trajectory during the field goal attempt.