Question

Oh football player kicks a football from the height of 4 feet with an initial vertical velocity of 64 ft./s use the vertical motion model H equals -16 tea to the power of 2+ VT plus S where V is initial velocity and feet per second and S is the height and feet to calculate the amount of time the football is in the air before it hits the ground round your answer to the nearest 10th if necessary.

Answer 1

Answer:4.1

Explanation:

Answer 2

Answer:

4.1 seconds

Explanation:

The height of the football is given by the equation:

$H = -16t^2 + V*t + S$

Using the inicial position S = 4 and the inicial velocity V = 64, we can find the time when the football hits the ground (H = 0):

$0 = -16t^2 + 64*t + 4$

$4t^2 - 16t - 1 = 0$

Using Bhaskara's formula, we have:

$\Delta = b^2 - 4ac = (-16)^2 - 4*4*(-1) = 272$

$t_1 = (-b + \sqrt{\Delta})/2a$

$t_1 = (16 + 16.49)/8 = 4.06\ seconds$

$t_2 = (-b - \sqrt{\Delta})/2a$

$t_2 = (16 - 16.49)/8 = -0.06\ seconds$

A negative time is not a valid result for this problem, so the amount of time the football is in the air before hitting the ground is 4.1 seconds.