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Despite the miserable NY Jets record this season, Sam Darnold, their QB, is still one of the best QBs in the NFL. His throw can reach 50 mph. If his throwing motion covers 1.2 m from the position where his arm starts to make a forward motion to the release position, and the mass of the ball is 15 ounces,

(a) What is the acceleration of the ball?
(b) How long did it take him to throw the ball (from the position where his arm starts to make a forward motion to the release position)?
(c) What is the force he exerted on the ball?
(d) Calculate the acceleration (deceleration) of the ball during that time.
(e) What is the force the wide receiver exerted on the ball?

User Kandan
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Final answer:

To find the acceleration, time, force, and deceleration of the football, we can use the relevant formulas from physics. Additionally, the force exerted by the wide receiver can be determined using Newton's third law. By substituting the given values and solving the equations, we can find the answers to the questions.

Step-by-step explanation:

To find the acceleration of the ball, we can use the formula a = (v^2 - u^2) / 2s, where v is the final velocity, u is the initial velocity, and s is the displacement. In this case, the displacement is 1.2 m and the initial velocity is 0 m/s (assuming the ball starts from rest). The final velocity can be found using the formula v = u + at, where t is the time taken to throw the ball. Rearranging the formulas, we have a = (v^2 - 0^2) / (2 * 1.2). By substituting the value of v and solving the equation, we can find the acceleration of the ball.

To find the time taken to throw the ball, we can rearrange the formula v = u + at to get t = (v - u) / a. Substitute the values of v, u, and a into the formula, and we can find the time taken.

The force exerted on the ball can be calculated using the formula F = ma, where F is the force, m is the mass of the ball, and a is the acceleration of the ball. By substituting the values and solving the equation, we can find the force exerted on the ball.

The acceleration (deceleration) of the ball during the time can be found by dividing the change in velocity by the time taken. The change in velocity can be calculated using the formula v - u. By substituting the values and solving the equation, we can find the acceleration (deceleration) of the ball.

The force the wide receiver exerts on the ball can be determined by using Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. Therefore, the force exerted on the ball by the quarterback is equal in magnitude but opposite in direction to the force exerted on the ball by the wide receiver.

User Shi XiuFeng
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