Question

Lacie kicks a football from ground level at a velocity of 13.9 m/s and at an angle of 25.0° to the ground.How far will the football travel before it lands? Round your answer to the nearest tenth.

Answer 1

it will be in the air 1.2 seconds and the football will travel 15.1 meters

Explanation:

Answer 2

First split up the velocity into horizontal and vertical components.

`v_x = 13.9 cos (25) \\ \\ v_y = 13.9 sin (25)`

Next set up position functions for both 'x' and 'y' directions.
Using the general position function

`(a)/(2) t^2 +vt + c`
a = acceleration, v = velocity, c = initial position

Assume initial position is at (0,0)
We know the velocities, vx and vy
acceleration due to gravity is -9.8 (Only in 'y' direction)
There is 0 acceleration in the 'x' direction.


`x(t) = 13.9 cos (25) t \\ \\ y(t) =-(9.8)/(2) t^2 + 13.9 sin(25) t`

The football will hit the ground when y(t) = 0

`-(9.8)/(2) t^2 + 13.9 sin(25) t = 0 \\ \\ -(9.8)/(2) t + 13.9 sin(25) = 0 \\ \\ t = ((2)(13.9 sin (25)))/(9.8)`

Substitute this value into x(t) to find how far the football traveled.

`x(t) = 13.9 cos(25) (((2)13.9 sin(25))/(9.8)) = (13.9^2 cos (25) sin(25))/(4.9)`