+28 A baseball is thrown upward at a velocity of 36 feet per second from a height of 7 feet. The equation to represent the height (h) after t seconds is h=−16t2+36t+7. How long before the ball hits the ground? (Round to the nearest hundredth of a second.)
+9481 h = -16t2 + 36t + 7
We want to find the time when the height is 0 .
So plug in 0 for h and solve for t .
0 = -16t2 + 36t + 7 Let's use the quadratic formula to solve this.
t = \(\frac{-36\pm\sqrt{36^2-4(-16)(7)}}{2(-16)}\)
t = \(\frac{-36\pm\sqrt{1296+448}}{-32}\)
t = \(\frac{-36\pm\sqrt{1744}}{-32}\)
t = \(\frac{-36+\sqrt{1744}}{-32}\) ≈ -0.18 or t = \(\frac{-36-\sqrt{1744}}{-32}\) ≈ 2.43
It will take about 2.43 seconds for the ball to hit the ground.
