This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
You're on a roll — Step 1: Identify the given height function. The height of the ball is given by the quadratic function: h(t) = -16t^2 + 40t + 1.5 This is a parabola opening downwards (since the coefficient of t^2 is negative), so its vertex represents the maximum height. Step 2: Find the time t at which the maximum height occurs. For a quadratic function in the form at^2 + bt + c, the time at which the maximum (or minimum) occurs is given by the formula t = -(b)/(2a). In this equation, a = -16 and b = 40. t = -(40)/(2(-16)) t = -(40)/(-32) t = (40)/(32) t = (5)/(4) seconds t = 1.25 seconds Step 3: Calculate the maximum height by substituting the time t back into the height function. Substitute t = (5)/(4) into h(t): h((5)/(4)) = -16((5)/(4))^2 + 40((5)/(4)) + 1.5 h((5)/(4)) = -16((25)/(16)) + (200)/(4) + 1.5 h((5)/(4)) = -25 + 50 + 1.5 h((5)/(4)) = 25 + 1.5 h((5)/(4)) = 26.5 The maximum height is 26.5 feet. The maximum height is 26.5 ft. Got more? Send 'em!