How Many Revolutions Does a Football Make in a Perfect Spiral Pass?

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To determine how many revolutions a football makes during a perfect spiral pass, first calculate the time the ball is in the air using its launch speed and angle. The horizontal and vertical components of the throw must be analyzed to find the total flight time. Once the time of flight is established, multiply it by the spin rate of 7.04 revolutions per second to find the total revolutions. The discussion emphasizes the importance of correctly applying kinematic equations and understanding the relationship between linear and rotational motion. Accurate calculations will yield the total number of revolutions made by the football while airborne.
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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 7.04 rev/s. In addition, the ball is thrown with a linear speed of 21.6 m/s at an angle of 47.0° 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?

I translated 47.0 degrees into radians and 7.04 into radians per sec and then used the rotational kinematics equation angle theta = 1/2 (omega initial - omega) * t, and then i multiplied t by 7.04 rev/sec... what am i doing wrong?? help! thanks
 
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Start by figuring out how long the football is in the air.
 

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