Answer
A) 2 seconds
B) What is the initial height of the diver? 10 m (above the surface)
What is the height after 3 seconds? 20 meters below the surface
Explanation
A) The height, h, in meters of a diver, t, seconds after diving off a platform can be modeled by:
When the diver hits the water's surface the height is 0 meters, that is, h(t) = 0.
We can solve this equation with help of the quadratic formula with the coefficients a = -5, b = 5, and c = 10, as follows:
![\begin{gathered} t_(1,2)=(-b\pm√(b^2-4ac))/(2a) \\ t_(1,2)=\frac{-5\pm\sqrt{5^2-4\cdot(-5)\operatorname{\cdot}10}}{2(-5)} \\ t_(1,2)=(-5\pm√(225))/(-10) \\ t_1=(-5+15)/(-10)=-1 \\ t_2=(-5-15)/(-10)=2 \end{gathered}]()
Given that variable t measures time, then the negative result has no sense and it is discarded.
Therefore, it takes the diver 2 seconds to hit the water's surface
B) What is the initial height of the diver?
At the initial height, t = 0. Substituting this value into the formula, we get:
The initial height is 10 meters.
What is the height after 3 seconds?
Substituting t = 3 seconds into height's formula, we get:
The height after 3 seconds is 20 meters below the surface.