The wheel in figure has eight equally spaced spokes and of `30 cm`. It is mounted on a fixed axle and is spinning at `2.5 rev//s`. You want to shoot a `20-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 and the spokes are very thin. What minimum speed must the arrow have ?
.

Options

A. `3.50 m//s`
B. `2.5 m//s`
C. `5.0 m//s`
D. `4.0 m//s`

Answer

D

Explanation

(d) To avoid touching the spokes, the arrow must go through the wheel in not more than
`Delta t=(1//8 rev)/(2.5 rev//s) =0.050 s`
The minimum speed `o` the arrow is then
`a_(min) =(20 cm)/(0.050 s) = 400 cm//s = 4.0 m//s`.