Question

HW02#2 Four Projectiles Four projectiles are all shot over level ground. The projectiles are launched at four different angles, 20, 30, 45° and 60° above horizontal. There are four steps for this problem: A. Intuition, B. Computation, C. Validation, and D. Discussion 5° Intuition: In the table, use your intuition (not computations!) to evaluate the greatest "G" and least "L" scenarios for the set of 4 angles below for the following criteria (1) same horizontal range, (2) same maximum height, and (3) same initial velocity. Note: you can assume the initial velocities will be automatically adjusted based on the criteria. A. 30° 20° Same Max Height Or 20 30 45° 60 20 30 45 60 20 30 45 60 Same Range 00m Same Initial Speed 30 m/s Angles Which has the greatest/l initial horizontal velocitv? Which has the greatestleast initial vertical Which has the greatest/least initial Which has the greatest/least time in the air? east Use "G for greatest, "L " for least and "S"if all are the same B. Computation: For each angle/criteria, use an analytical tool of your choice (i.c. Excel, Matlab) to compute the a. Total Initial Velocity b. Initial Horizontal Velocity c. Initial Vertical Velocity d. Time to impact e. Max height f. Range (distance traveled horizontally) C. Validation: Now visit h and check your answers. You can show the numerical results by clicking the bottom check box. This won't have all the variables asked for in B, but enough where you can check your work. D. Discussion I. Where was your intuition incorrect (between parts A and B)? Which criteria (range, height, or speed) did you find to be the most challenging? Why? Which was the only case where the greatestleast was the lowest or highest angles? How can you explain this For the same initial speed criteria two of the projectiles have the same range, how can this be? Can you form a general rule about angles where this would hold true? 2. 3. anomaly? 4. Turn in the problem like a short lab report with results from Parts A, B, and D

Answer 1

Please find the attachment.

a) Intuition max. range} implies v_0^2/g v_0 = 31.3 m/s same range mu_max = mu^2 sin^2 theta/2g mu = v_0^2/2g same max height (v_x = u_x_0) v_u^� = 2g y + v_0^2 same initial speed Computation a) Total initial velocity implies sigma v_0 implies 33.89 m/s (Avg of all readings) (b) Total horizontal velocity implies sigma v_x implies 30.42 m/s (c) Total vertical velocity implies sigma v_y implies 27.76 m/s (d) Time to impact implies 2v_0 sin theta/g implies 2.86 m/s (e) Max height implies H = v_0^2/2g implies 58.5 m.H (H) Range implies v_0^2/g implies 117.07m = Range Discussion (i) considering the horizontal and vertical velocities as same for all the projection - given out in accurate calculation (ii) speed is the most challenging - thus we not have the enough clarity on time rest (Range, height) we easily calculate (iii) In speed - both vertical velocity greatest/least is equivalent to initial speed (iv) yes for (31.32 & 33.10) - range