Velocity & Components

Cock Back

From the data we collected, we know the horizontal displacement (0.61m) and vertical displacement (0.254m) of the ball when he is cocking the ball back. We also know the time (0.43s) from when he has the ball at rest to when he brings the ball back behind his head. Since we have the displacements and the time from when the ball is at rest to when it at the back of his head, we can calculate the horizontal velocity and vertical velocity of the ball. We can then use kinematics equations, trigonometry and Pythagorean theorem to determine the final vertical component and the actual velocity when he cocks the ball back. Because we start the ball at rest the initial horizontal velocity and the initial vertical velocity is 0m/s.

Horizontal Velocity

Vertical Velocity

Therefore the horizontal velocity when he is cocking the ball back is 2.8m/s (up)

Therefore the vertical velocity when he is cocking the ball back is 1.2m/s (left)

Therefore the velocity when he is cocking the ball back is 3.4m/s (57º above horizontal)

Velocity

Throw

From the data we collected, we know how far the ball traveled, which gives us the horizontal displacement (9.02m). We also know the time (1.03s) from when the ball left his hand to when I caught the ball. Since we have the horizontal displacements and the total time from when the ball left his hand and into my hand. We can calculate the initial and final horizontal velocity, also the initial and final vertical velocity of the throw. We can then use kinematics equations, trigonometry and Pythagorean theorem to determine the actual velocity when he throws the ball and when I caught it.

To find initial vertical velocity, I set the final vertical velocity to 0, because at max height the football does not travel vertically anymore. this is also why the time is cut in half, because it takes half the time for the ball to reach max height.

Initial Velocity

Initial Vertical Velocity

Initial Horizontal Velocity

To find the initial horizontal velocity, i set the accelelation to 0 because the football does not a accelelate horizontally when it's lanches.

Therefore the initial vertical velocity when he throws the ball is 5.05m/s (up)

Therefore the initial horizontal velocity when he throws the ball is 8.8m/s (right)

Therefore the initial velocity when he throws the ball is 10.1m/s (30º above horizontal)

Final Velocity

Since horizontal velocity is constant during projetile motion. the final horizontal velocity is the same as intial horizontal velocity. now we know the horizontal velocity do not change we can solve for the final vertical velocity using the initial vertical velocity and acceleration equation. Finally, we can find the angle at which I caught the ball using trigonometry.

Therefore the final vertical velocity when he throws the ball is 5.05m/s (down)

Therefore the final velocity when he throws the ball is 10.1m/s (down)(30º below horizontal)