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Pluorminus Arrow Hits Apple An arrow is shot at an angle of theta = 45 degree ab

ID: 1654944 • Letter: P

Question

Pluorminus Arrow Hits Apple An arrow is shot at an angle of theta = 45 degree above the horizontal. The arrow hits a tree a horizontal distance D = 220 m away, at the same height above the ground as it was shot. Use g = 9.8 m/s^2 for the magnitude of the acceleration due to gravity. Part A Find t_a, the time that the arrow spends in the air. Answer numerically in seconds, to two significant figures. Suppose someone drops an apple from a vertical distance of 6.0 meters, directly above the point where the arrow hits the tree. Part B How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree?

Explanation / Answer

Range of same level projectile = v^2 sin(2 theta) / g

220 = v^2 sin(45 x 2) / 9.8

v = 46.4 m/s

(A) time of flight, t = 2 v sin(theta) / g


t = 2 x 46.4 x sin45 / 9.8

t = 6.7 sec

(B) time taken by apple to drop by 6 m .
  
y = v0y t + a t^2 /2

6 = 0 + 9.8 t^2 /2

t = 1.11 sec

t1= 6.7 - 1.11 = 5.60 s