The furthest distance the quarterback could throw the ball neglecting air resistance is 81.63 meters.
The situation given above is an example of projectile motion.
The maximum distance up to which a projectile can be thrown is known as its range, which is given by the formula,
Range(R) = 2u^2 sin(2θ)/g
Here u is the maximum velocity of the projectile= 20 m/s
θ is the angle at which the projectile is launched = 45°
g is the acceleration due to gravity = 9.8 m/s^2
Putting the above values in the given equation,
The range comes out to be 81.63 meters.
Hence, the furthest distance the quarterback could throw the ball neglecting air resistance is 81.63 meters.
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