Question

laurie throws a tennis ball toward her dog from a height of 4.5 ft. the initial vertical velocity of the ball is 18 ft/s. at the same time as laurie throws the ball, her dog jumps with an initial vertical velocity of 21 ft/s. when the dog jumps, its mouth is 1.5 ft above the ground. which system models the height of the tennis ball and the height of the dogs mouth over time? h = 4.5t + 18 and h = -16t² + 1.5t + 21 h = 18t + 4.5 and h = -16t² + 21t + 1.5 h = -16t² + 4.5t + 18 and h = -16t² + 1.5t + 14 h = -16t² + 18t + 4.5 and h = -16t² + 21t + 1.5 projectile motion formula: h = -16t² + vt + h₀ t = time, in seconds, since the ball was thrown h = height, in feet, above the ground

Explanation:

Step1: Analyze the tennis ball's height formula

For the tennis ball, the initial height \(h_0 = 4.5\) ft and initial velocity \(v = 18\) ft/s. Using the projectile - motion formula \(h=-16t^{2}+vt + h_0\), we substitute the values. So the height formula for the tennis ball is \(h=-16t^{2}+18t + 4.5\).

Step2: Analyze the dog's mouth height formula

For the dog's mouth, the initial height \(h_0 = 1.5\) ft and initial velocity \(v = 21\) ft/s. Using the projectile - motion formula \(h=-16t^{2}+vt + h_0\), we substitute the values. So the height formula for the dog's mouth is \(h=-16t^{2}+21t + 1.5\).

Answer:

\(h=-16t^{2}+18t + 4.5\) and \(h=-16t^{2}+21t + 1.5\)