A ball is thrown upward with an initial velocity of 40 feet per second from ground level. The height of the ball, in feet, after t seconds is given by h= -16t^2 + 40t. At the same time, a balloon is rising at a constant rate of 10 feet per second. Its height, in feet, after t seconds is given by h = 10t. Find the time it takes for the ball and the balloon to reach the same height and explain.

It takes 1.875 seconds for the ball and the balloon to reach the same heightStep-by-step explanation:A ball is thrown upward with an initial velocity of 40 feet per second from ground levelThe height of the ball, in feet, after t seconds is given by h= -16 t² + 40 tAt the same time, a balloon is rising at a constant rate of 10 feet per secondIts height, in feet, after t seconds is given by h = 10 tWe need to find the time it takes for the ball and the balloon to reach the same height∵ The height of the ball is given by h = -16 t² + 40 t∵ The height of the balloon is given by h = 10 t∵ They start at the same time t∵ They have the same height hEquate the two equations of h to find t∴ -16 t² + 40 t = 10 t- Subtract 10 t from both sides∴ -16 t² + 30 t = 0- Take -2 t as a common factor∴ -2 t(8 t - 15) = 0Equate -2 t by 0 and 8t - 15 by 0∵ -2 t = 0 ⇒ divide both sides by -2∴ t = 0 ⇒ initial time∵ 8 t - 15 = 0 ⇒ add 15 to both sides∴ 8 t = 15 ⇒ divide both sides by 8∴ t = 1.875 secondsIt takes 1.875 seconds for the ball and the balloon to reach the same heightLearn more:You can learn more about the equations in brainly.com/question/2977815#LearnwithBrainly