Sapling Learning You would like to shoot an orange in a tree with your bow and a

Question

Sapling Learning You would like to shoot an orange in a tree with your bow and arrow. The orange is hanging 5.00 m above the ground. On your first try, you fire the arrow at 36.0 m/s at an angle of 30.0 above the h height of 1.40 m while standing 53.0 m away. Treating the arrow as a point from a 30.0 5.00 m and neglecting air resistance, what ht of the arrow once it has 1.40 m traveled the 53.0 m horizontally to the tree? 53.0 m in If you fire at the same speed and angle on your second try, how far away could you arrows 108 m 99.8 m 612m 14 8 m 66 m

Explanation / Answer

launch velocity v = 36 m/s

projectile angle = 30 deg

horizontal component of velocity vx = 36 Cos(30) = 31.18 m/s

vertical component vy = 36Sin(30) = 18 m/s

horizontal motion x = vx t = 31.18t ( no external force in horizontal direction)

when the arrow reaches the orange x = 53 m

= 31.18 t

t = 1.7 s

vertical motion

y = vy t -gt2 /2 = 18t -4.9t2 ( when the arrow travelled 53 m t = 1.7s)

= 18*1.7 -4.9*1.72  

= 16.44 m

height h = 1.4 +y ( inital height = 1.4 m

= 17.84 m

b) 18t -4.9t2 = 5-1.4 , so that the arrow reaches the orange

t = 0.21s

horizontal distance traveled x = 0.21 *31.18 = 6.62 m

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