Question

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3.2 The girl shoots a basketball with velocity vA and angle 8 (-30°) to horizontal. Choos- ing coordinates as shown, the relative height of the basket is H = hg-hs, and the basket is a distance R from the shot. 7 777777777777777777 (a) Derive an expression for the initial velocity in terms of the parameters (9, R, H, 6). (b) Compute va for R = 25 ft, H = 6 ft, 8 = 30°, and g = 32.2 ft/s?. A: 40 ft/s (e) Change the angle to 8 73.4º. Do you get a similar value for 2

Answer 1

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now from the given figure a x= utt. Lath R = (y cosest to In y-Direction H = VA Sino. t - fxgxt ² H = RVA Sino. R 89/R P coso - 4. & 1 x ( 4 colo) 3 H = Rtanoag R² secro ZVA RTano-t = 9R Secro g 1:9--9.81] .-9.811 ZVAY VA = 9R Secro 2(Rtano-4) 9R Secro - VA = 1 2CRTaNO-H) R625ft, H=6ft, o=38 and 9=32.2 Hys - VA = 132.2 x 25 x 1.333 2(25x0.577-6) VA = 39.8852 Flisec r IVA = 40 ft/sec - ② 16 0= 73.4 2) VA = 32.2x25% 12-28228 V 2 (25x8.3544-6) » XA = 39.7924 ft/sec ~ [VA = 40 ft/sec Yes, initial velocity in case 6 and care almost equal (approssmarely). are