MATH SOLVE

2 months ago

Q:
# 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.

Accepted Solution

A:

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