Mathematics, 19.12.2019 18:31 kamnicole13
Aball is thrown vertically upward from the top of a building with an initial velocity of 96 feet per second. the ball's h height after t seconds is given by the equation h = −16t2 + 96t + 100. how long will it take for the ball to hit the ground? (to the nearest tenth of a second)
a) 5.9 seconds
b) 6.3 seconds
c) 6.9 seconds
d) 7.2 seconds
Answers: 1
![-16t^2+96t+100=0\ \ [\text{Divide by -4}]\\ \\4t^2-24t-25=0\ \ [\text{In this quadratic equation }a=4,\ b=-24,\ c=-25]\\ \\D=b^2-4ac=(-24)^2-4\cdot 4\cdot (-25)=576+400=976\\ \\t_{1,2}=\dfrac{-b\pm\sqrt{D}}{2a}=\dfrac{-(-24)\pm\sqrt{976}}{2\cdot 4}=\dfrac{24\pm4\sqrt{61}}{8}\approx -0.9,\ 6.9](/tpl/images/0426/2054/d9278.png)
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