Our class was given the task to collaborate on a lab to find the distance a ball would go when fired and place a target where we believed it would land. The class was allowed to fire the ball once, then the ball would be moved and the angle would change. Together, we took measurements of the first setup, and started doing calculations. We worked in small groups and compared answers, coming to a conclusion that the initial velocity of the ball was around 4.65 m/s. This allowed us to start to calculate the distance the ball would travel at the new height and angle.
However, the class was running out of time and out of desperation, the book was placed at a randomly predicted location and the ball was fired. It missed the target slightly. We were told to redo the calculations and find out what went wrong. The problem was that the target was placed without finishing the calculations, and therefore there was little chance for us to be right.
The initial velocity was 4.65 m/s, and the ball was being fired at -4 degrees, meaning that the ball started with a horizontal velocity of 4.64 m/s and a vertical velocity of .32 m/s. The accelerations for the two directions were 0 m/s2 (horizontal) and 9.8 m/s2 (vertical). The vertical displacement would be 1.035 m once the ball was fired.
The equation y = vot + (1/2)at2 allowed me to determine the time the ball would take when traveling to the target. I used the quadratic formula, which gave me .43 s and -.496 s. The negative time was discarded as time cannot be negative. I then used the same equation (x = vot + (1/2)at2) to find the distance the ball would travel, which was 1.995 m.