Question

modeling the quadratic equation of a linear - quadratic system
cheryl and daryl are circus performers. a cable lifts cheryl into the air at a constant speed of 2 ft/s. when cheryl’s arms are 12 ft above the ground,
daryl throws her a ball. he throws the ball from a height of 6 ft with an initial vertical velocity of 24 ft/s.
t = time, in seconds, since the ball was thrown
h = height, in feet, above the ground
projectile motion formula:
h = - 16t²+vt + h₀
the thrown ball is a projectile, so its height, h, in feet, after t seconds can be modeled using the projectile motion formula. complete the equation that models the ball’s height.

Explanation:

Step1: Identify formula variables

The projectile motion formula is $h = -16t^2 + vt + h_0$, where:

• $-16$ is the gravitational constant term,
• $v$ = initial vertical velocity,
• $h_0$ = initial height.

Step2: Substitute given values

From the problem: $v=24$ ft/s, $h_0=6$ ft. Substitute into the formula:
$h = -16t^2 + 24t + 6$

Answer:

$h = -16t^2 + 24t + 6$