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 5.8 rev/s.

In addition, the ball is thrown with a linear speed of 17 m/s at an angle of 53° 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

To find the total number of revolutions, first calculate the time of flight for the football using the projectile motion formula, then multiply this time by the rotational speed of 5.8 rev/s.

Step-by-step explanation:

The question asks us to find out how many revolutions a football makes in the air given that it spins at 5.8 revolutions per second (rev/s) and is thrown with a linear speed of 17 meters per second (m/s) at an angle of 53° to the ground. To answer this, we need to calculate the time of flight of the football and then multiply that time by the rotational speed of the football.

The time of flight for a projectile launched at an angle θ and speed v is determined by the formula: t = (2*v*sin(θ))/g, where g is the acceleration due to gravity (9.8 m/s2). Once we have the time of flight, multiplying it by the rotational speed gives us the total number of revolutions.