Question

a) Consider a coordinate system where the x and y coordinates are both zero when the ball passes through the pivot and lands on the top of the table at that same level (y = 0). The ball then starts at y = 0 and reaches y = 0 again when landing on the table. The range R will simply be the x coordinate where it hits. Draw your theoretical quantitative predictions for the range R as a function of the initial angle α of 15◦ , 30◦ , 45◦ , 60◦ , 75◦ on the following graph. Make sure the points are correct relative to each other. Assume there is no air resistance.

Enter your predictions on the graph assuming the range at 45^○ is 9 (enter that point as well). That is the point with coordinates (45,9) is your reference point for the range at 45^○and you are required to calculate the missing coordinates for the points (15, range at 15^○ w.r.t. range at 45^○), (30, range at 30^○ w.r.t. range at 45^○), etc.

b) Draw your quantitative predictions for the trajectory on the following graph for 15◦ , 30◦ , 45◦ , 60◦ , 75◦ . (These will be lines of motion.) Assume there is no air resistance.

Answer 1

R = u^2 sin 2 theta/g theta = alpha R_1 = u^2/g (sin 2(15 degree)) R_1 = u^2/g times 0.5 R_2 = u^2/g times sin 60 degree = u^2/g times 0.866 R_3 = u^2/g sin 90 degree = u^2/g R_4 = u^2/g sin 120 degree = u^2/g times 0.266 R_5 = u^2/g sin 150 degree = u^2/g times 0.50 R_3 = 9 rightarrow u^2 = 9 times 9.81 u = 9.3 g R_1 = 4.5 R_2 = 7.74 R_3 > R_4 = R_2 > R_1 = R_5 R_3 = 9 R_4 = 7.794 R_5 = 4.5