Question

The height h in feet of a person on a waterslide is modeled by the function h(t)= -0.025t^2-0.5t+50, where t is the time in seconds. At the bottom of the slide, the person lands in a swimming pool. To the nearest tenth of a second, how long does the ride last?

Answer 1

Time of ride satisfies the condition $h(t)= -0.025t^2-0.5t+50=0$. Since the time of ride is not less than ,

the solution $t_1=\frac{0.5+\sqrt{0.5^2+4\cdot 0.025\cdot 50}}{-0.025*2}<0$ cannot be the time of ride.

So the time of ride is $t_2=\frac{0.5-\sqrt{0.5^2+4\cdot 0.025\cdot 50}}{-0.025*2}=\frac{-0.5+\sqrt{5.25}}{0.05}\approx 35.8$ seconds