You fire an arrow parallel to the ground at a rotating target. The arrows initia

Question

You fire an arrow parallel to the ground at a rotating target. The arrows initial height is level with the target's axle. The target is broken into nine equally sized wedges and each of the wedges are sequentially numbered. The #1 wedge is located at the top of the target, when the arrow is fired. At the same instant as the arrow is fired, the target rotates from rest with an angular acceleration, =106 rev/min2 , (the wedge's pass in sequential order 1 2 3 … ). If the arrow has an initial speed of 50 m/s, and is fired at a distance of 100m, which numbered wedge will the arrow hit?

Explanation / Answer

Here ,

speed , u = 50 m/s

distance , d = 100 m

time taken to travel the arrow

t = 100/50 = 2 s

angular acceleration ,a = 106 rev/min^2

a = 0.02944 rev/s^2

angle rotated = 0.5 * a * t^2

angle rotated = 0.5 * 0.02944 * 2^2

angle rotated = 0.0588 rev

angle of each section = 1/9 = 0.111 rev

hence , the arrow will hit the 1st number wedge

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