Question

cheryl has now been lifted to a platform. again, daryl throws a ball from a height of 6 ft with an initial vertical velocity of 24 ft/s. at the same time, cheryl throws the ball she caught earlier. she throws her ball from a height of 24 ft with an initial vertical velocity of 6 ft/s so that it hits daryls ball. t = time, in seconds, since the balls were thrown h = height, in feet, above the ground projectile motion formula: h = -16t² + vt + h₀ which system of equations models this situation correctly? h = -16t² + 24t + 6 h = 6t + 24 h = -16t² + 24t - 6 h = -16t² + 6t - 24 h = -16t² + 24t + 6 h = -16t² + 6t + 24 done

Explanation:

Step1: Analyze Daryl's ball

For Daryl's ball, the initial height \(h_0 = 6\) ft and initial velocity \(v = 24\) ft/s. Using the projectile motion formula \(h=-16t^{2}+vt + h_0\), we substitute the values. So, \(h=-16t^{2}+24t + 6\).

Step2: Analyze Cheryl's ball

For Cheryl's ball, the initial height \(h_0 = 24\) ft and initial velocity \(v = 6\) ft/s. Using the projectile motion formula \(h=-16t^{2}+vt+h_0\), we substitute the values. So, \(h=-16t^{2}+6t + 24\).

Answer:

\(h=-16t^{2}+24t + 6\) and \(h=-16t^{2}+6t + 24\) (the third option in the given choices).