Question

I am watching the Super Bowl. With 12 minutes and 17 seconds left in the 3rd quarter, Tom Brady throws the ball from the 13-yard line. Gronkowski moves into position 2 yards inside the end zone. He catches the ball at 12 minutes and 16 seconds.

A. Approximately how fast did Brady throw the ball? Report your answer in miles per hour and ignore the vertical motion of the ball.
B. What is the acceleration of Brady's arm if he moves the ball 1 meter while throwing.
C. How long does it take for Brady to complete the throw?

Answer 1

Solution

Let us go to the basics first

This question is based on the concept of

1. Uniform motion

2. Accelerated motion

3. Newton's equation of motion

The detailed solution is described below

Part (A) Speed of the ball thrown by Brady

= Distance / time

= 13 yard / 1 second

= 13 yards/second

= 13 * 2.045 miles per hour

= 26.6 miles per hour. (ANSWER PART A)

Part (B) Acceleration of Brady's arm will be given by following Newton's equation

v^2 = 2 as (when initial velocity is zero)

(v = 26.6 miles per hour = 11.88 m/s)

Thus, acceleration a = v^2 / 2s

= (11.88)^2 / (2*1)

= 70.57 m/s^2 (Answer part B)

Part (c)

Again from Newton's equation

V = at (when initial velocity is zero)

Thus, t = V/a = 11.88/70.57

= 0.17 seconds (Answer part C)

THANKS!!!