Question

The wheel in the figure has eight equally spaced spokes and a radius of 39 cm. It is mounted on a fixed axle and is spinning at 1.1 rev/s. You want to shoot a 25-cm-long arrow parallel to this axle and through the wheel without hitting any of the spokes. Assume that the arrow and the spokes are very thin. What minimum speed must the arrow have?

Answer 1

Suppose time taken by wheel to complete one rotation is 'T', then

for time for arrow to go through the wheel without hitting any of the spokes will be (T/8),

So in this time wheel will complete 1/8 rev = 0.125 rev

Now given that speed of wheel = 1.1 rev/sec, So

time = angular displacement/angular speed

time = 0.125 rev/(1.1 rev/sec) = 0.114 sec

Now in this time arrow must pass through wheel, and given that length of arrow is 25 cm, So

Minimum Speed = length of arrow/time in which arrow needs to pass through spokes

Minimum Speed = 0.25 m/0.114 sec

Minimum speed = 2.19 m/sec

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