Question

In a football game a kicker attempts a field goal. The ball remains in contact with the kicker's foot for a time of t = 0.050 s,during which time it experiences an acceleration of a = 340 m/s². The ball is launched at an angle of θ = 51 degrees above ground. Determine the horizontal and vertical components of the launch velocity. Neglect acceleration due to gravity for this problem

Answer 1

The horizontal component of the football's launch velocity is approximately 10.77 m/s, and the vertical component is approximately 13.24 m/s, calculated using the given acceleration and the angle of launch.

Step-by-step explanation:

To determine the horizontal and vertical components of the launch velocity of a football kicked at an angle 51 degrees above the ground with an acceleration of 340 m/s² for a duration of 0.050 s, we must first calculate the final velocity using the formula v = a × t, where a is acceleration and t is the time. Here, v = 340 m/s² × 0.050 s = 17 m/s. Then, we can find the horizontal (vx) and vertical (vy) components using trigonometric functions: vx = v × cos(θ) and vy = v × sin(θ).

The horizontal component is: vx = 17 m/s × cos(51°) ≈ 10.77 m/s.
The vertical component is: vy = 17 m/s × sin(51°) ≈ 13.24 m/s.