Question

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

Answer 1

Answer:

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

b) 480 ft

c) 64 ft

Step-by-step 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 = $\frac{-64}{2(-16)} =2$

Substituting t = 2 in the y equation:

y = 64(2) - 16(2)² = 128 - 64 = 64 ft

y = 64 ft