Problem 1.16 - Problem 1.16 [Difficulty: 3] Given: Long bow...

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Problem 1.16 [Difficulty: 3] Given: Long bow at range, R = 100 m. Maximum height of arrow is h = 10 m. Neglect air resistance. Find: Estimate of (a) speed, and (b) angle, of arrow leaving the bow. Plot: (a) release speed, and (b) angle, as a function of h Solution: Let Vu iv jV i j ) 00 0 =+= + 0 ±± (cos ± sin ± θθ Σ Fm m g y dv dt == , so v = v 0 – gt, and t f = 2t v=0 = 2v 0 /g Also, mv dv dy mg, v dv g dy, 0 v 2 gh 0 2 =− Thus hv2 g 0 2 = (1) Σ du dt 0, so u u const, and R u t 2u v g f x = = = = (2) From Eq. 1: v 2gh 0 2 = (3) From Eq. 2: u gR 2v gR 22 g h u gR 8h 0 0 0 2 2 = Then 2 1 2 0 2 2 0 2 0 2 0 8 2 and 2 8 + = + = + = h gR gh V gh h gR v u V (4) s m 7 . 37 m 10 1 m 100 s m 8 81 . 9 m 10 s m 81 . 9 2 2 1 2 2 2 2 0 = × × + × × = V From Eq. 3: v2 g h V s i n s i n
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Problem 1.16 - Problem 1.16 [Difficulty: 3] Given: Long bow...

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