Question

A quarterback throws a pass that is a perfect spiral. In other words, the football does not wobble, but spins smoothly about an axis passing through each end of the ball. Suppose the ball spins at 8.8 rev/s. In addition, the ball is thrown with a linear speed of 19 m/s at an angle of 59° with respect to the ground. If the ball is caught at the same height at which it left the quarterback's hand, how many revolutions has the ball made while in the air?

Answer 1

Answer:

No revolutions = 29.16 rev

Explanation:

We had to determine the time of flight and then we needed to find no of revolutions ball made while in the air

by applying the second equation of motion

$V_{f} =V_{i}t+\frac{1}{2}at^{2}$

as the ball came to the same point after rising to height

$V_{f} =0$

The vertical component of the ball with initial velocity is given as$V_{i}=Vsin$Ф

$V_{i}=19sin59$

$V_{i}=15.66\frac{m}{s}$

here a= gravitational acceleration=$-9.8\frac{m}{s^{2} }$

• negative direction indicates opposite direction with respect to motion of body

$t=-\frac{2Vi}{-g}$

$t=3.3 sec$

No revolutions =8.8 x 3.2 = 29.16 rev