Question

Help!

A kicker punts a football from 3 feet above the ground with an initial velocity of 47 feet
per second
Write an equation that gives the height (in feet) of the football as a function of the time
in seconds) since it was punted.

Answer 1

The equation that gives the height of the football as a function of the time can be expressed as:

h = -16t^2 + 47t + 3

h = height. t = time

Answer 2

Explanation:

The height of the ball from the ground is 3ft. The initial velocity of the ball is 47 feet per second.

The height which the ball travels can be gotten from Newton's equation of motion,

h = ut + 1/2at^2

h = total height which the ball attains from the ground.

u = 47ft per second. initial velocity of the of the ball when it was kicked.

t = time it takes to attain the height

a = acceleration due to gravity and it is negative in this case since the ball is moving upwards against gravity. Let us assume acceleration due to gravity to be -32.17405 ft/s^2

h = 47t - 1/2 × 32.17405t^2

h = 47t -16.087025t^2

Since the ball was 3 feet above the ground,

h(t) = 47t -16.087025t^2 + 3