Football Game at UNTS Apogee Stadium: Calculate Horizontal Component of Launch Velocity

What is the horizontal component of the launch velocity in a football game at the UNTS Apogee Stadium?

Can the horizontal component of the launch velocity be determined from the given data?

Horizontal Component of Launch Velocity:

The horizontal component of the launch velocity in the football game at the UNTS Apogee Stadium is 10.71.

When a kicker attempts a field goal at the UNTS Apogee Stadium, the ball remains in contact with the kicker's foot for 51 seconds, experiencing an acceleration of 0.42 m/s^2. The ball is launched at an angle of 60 degrees above the ground. To calculate the horizontal component of the launch velocity, we can follow these steps:

1. Determine the magnitude of the launch velocity using the formula v = a * t, where: - v = launch velocity - a = acceleration (0.42 m/s^2) - t = time of contact (51 s)

Substitute the values into the formula: v = 0.42 * 51 = 21.42 m/s

2. Calculate the horizontal component of the launch velocity using the formula: v_x = v * cos(θ), where: - v_x = horizontal component of launch velocity - θ = launch angle (60 degrees)

Substitute the calculated values: v_x = 21.42 * cos(60°) = 10.71 m/s

Therefore, the horizontal component of the launch velocity in the football game at the UNTS Apogee Stadium is 10.71 m/s.