Theory: That kinematic equations are adequate for predicting the landing point of a ball, on an inclined board, and general motion of the ball through the air.
Procedure: Set up two V-tracks on top of our desk, so that a steel ball rolls consistently at the same velocity in the horizontal position, off of it; also measure the height of the desk (plus uncertainty). Using carbon paper to track where the ball lands on the ground, five times, measure how far from the desk it landed generally (plus uncertainty). Calculate the horizontal velocity, place a board up against the V-track so that the steel ball will strike the board as it falls, and calculate a prediction of where on the board the ball will strike (also do this five times). Measure the angle (plus uncertainty) of the inclined board, calculate the propagated errors and compare with your prediction.
*The Track was set up.
*The height of the track was measured to be y=94.2 +/- 0.1 cm
*After five trials the general distance of the ball's landing was measured to be x=66.3 +/- 0.2 cm.
*Since the original velocity in the vertical position is always zero in our model, we can calculate the time it takes for the ball to reach the ground using (y=0.5*g*t^2).
*Time is calculate to be 0.438 seconds.
*Since movement in the horizontal direction is independent from the vertical, we can generalize the velocity of the horizontal position using the time it took for the ball to fall and the distance it traveled in the horizontal direction in that time (V=x/t).
*V=1.51 m/s
*We placed a board to lean against the table, so that the ball would strike it before the floor, and measured the angle it created with the floor.
*Angle was 49 +/- 0.5 degrees.
*The distance(d) traveled on the board can be calculated in the x direction using x=d cos (angle), x also equals V*t, so set equal to each other, (t=(d cos angle)/V).
*Similarly d traveled on the board in the y direction can be expressed (y= d sin (angle)), y also equals 0.5*g*t^2, so set equal to each other and replacing t with the equation calculated in the previous bullet point. (d=(sin(angle)*V^2)/(0.5*g*cos(angle)^2)).
*We can now calculate d, its d=0.818 m.
*We performer the experiment five time to find the actual distance of d, its generally d=0.791 m.
*The propagated error can be calculated as (dd=sec(angle)*(uncertainty of x)+csc(angle)*(uncertainty of y)+ ((2V^2)/g)*(sec(angle)^2*sec(angle)+tan(angle)*sec(angle)*tan(angle))*(uncertainty of the angle)
*Its calculated to be dd=+/-0.026 m, which is within my predicted 0.818 m
Conclusion
*The actual was within my prediction and its propagated error, though barely, so I consider it a good model.
*Problems with the experiment itself, that it doesn't account for air resistance slowing the ball.
*Our process probably could have been better, say by averaging the five trials distances in the x direction, and on the board, instead of "generalizing" or approximating their position.
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