+0

# QUICK!

0
214
1
+171

A kicker punts a football from 3 feet above the ground with an initial velocity of 47 feet per second.

1.Write an equation that fives the height (in feet) of the football as a function of the time (in seconds) sunce it was punted.

2. Find the height (in feet) of the football 2seconds after the punt

3 Caculate how many seconds after the ball would hit the ground.

Thanks

BOSEOK  Aug 10, 2017
Sort:

#1
+91786
+1

A kicker punts a football from 3 feet above the ground with an initial velocity of 47 feet per second.

1.Write an equation that fives the height (in feet) of the football as a function of the time (in seconds) sunce it was punted.

This depends on the angle that the ball is kicked at.

Let up be positive vertical y direction.

If you let the acute angle between the horizonal and the initial direction of flight then

The initial vertical velocity is 47sin(theta)

The initial horizonal velocity is 47cos(theta)

$$\ddot y=-32 feet/sec\quad that \;is\;from\;gravity\\ \dot y=-32t+47sin\theta\\ y=-16t^2+(47sin\theta)t+3\\~\\$$

2. Find the height (in feet) of the football 2seconds after the punt

$$\text{When t=2}\\ y=-16*2^2+(47sin\theta)*2+3\\ y=-64+94sin\theta+3\\ y=-61+94sin\theta\;\; feet, \qquad \text{or 0 feet if this is negative}$$

3 Caculate how many seconds after the ball would hit the ground.

Find t when y=0

$$0=-16t^2+(47sin\theta)t+3\\ t=\frac{-47sin\theta\pm\sqrt{47^2sin^2\theta-4*-16*3}}{2*-16}\\ t=\frac{-47sin\theta\pm\sqrt{2209sin^2\theta+192}}{-32}\\ t=\frac{47sin\theta\pm\sqrt{2209sin^2\theta+192}}{32}\\ \theta \;\text{ is acute so}\\ t=\frac{47sin\theta+\sqrt{2209sin^2\theta+192}}{32}\;\;seconds$$

If the ball is kicked horizonally theta=0 and it will take 0.43 seconds to hit the ground.

If the ball is kicked vertically theta=90 degrees it will take 3.05 seconds to hit the ground.

Melody  Aug 13, 2017

### 11 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details