Question

The path of a soccer ball can be modeled by the parametric equation, where t is in seconds and distance are in feet.

a) when will the ball hit the ground?


b) how far did the ball travel?


c) find the maximum height of the ball. when does it count?

Answer 1

a) it takes 4 seconds for the ball to hit the ground

b) 480 ft

c) 64 ft

Explanation:

The parametric equation is

x(t) = 120t and y = 64t - 16t²

a) To find when the ball hits the ground, we use the y equation. The ball hits the ground at y = 0. Therefore:

`0=64t - 16t^2\\16t^2-64t=0\\16t^2=64t\\t=4`

t = 4 seconds,

Therefore, it takes 4 seconds for the ball to hit the ground

b) Since it takes 4 seconds for the ball to hit the ground, to find how far the ball would travel, we substitute t = 4 into x = 120t. Therefore:

x = 120(4) = 480

x = 480 ft

a) The maximum height of the ball is the vertex of the y equation.

The vertex occurs at t =
`(-64)/(2(-16)) =2`

Substituting t = 2 in the y equation:

y = 64(2) - 16(2)² = 128 - 64 = 64 ft

y = 64 ft