Question

While watching some tv you see a circus show in which a woman drives a motorcycle around the inside of a vertical ring. you determine that she goes around at a constant speed and that it takes her 4.0 seconds to get around when she is going her slowest. if she is going at the minimum speed for this stunt to work, the motorcycle is just barely touching the ring when she is upside down at the top. at that point she is in free fall. she just makes it around without falling off the ring; but what is she made a mistake and her motorcycle fell of at the top? how high us is she? would someone be hurt falling from this height?

Answer 1

Since the biker is moving at constant speed

so we will have

$v = \frac{distance}{time}$

here we know that

$distance = 2\pi R$

time = 4 second

now we have

$v = \frac{2\pi R}{4} = \frac{\pi R}{2}$

now at the top point it feels free fall

so it is

$mg = \frac{mv^2}{R}$

$v^2 = Rg$

$(\frac{\pi R}{2})^2 = Rg$

$R = \frac{4g}{\pi^2}$

so height of the bike at the top is same as diameter

$h = 2R$

$h = \frac{8g}{\pi^2} = 7.95 meter$

Yes it will hurt on falling from this height