Question

a diver dives from a 10 m springboard the equation f(t) = -4.9t² + 4t + 10 models her height above the pool at time in seconds.when does the diver enter the water? (That means that the diver will be at a height of 0)

Answer 1

When the diver enters the water her height will be zero, this means f(t) will be zero, that is,

$-4.9t^2+4t+10=0$

We can solve this equation with the help of the quadratic formula, as follows:

$\begin{gathered} t_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t_{1,2}=\frac{-4\pm\sqrt[]{4^2-4\cdot(-4.9)\cdot10}}{2\cdot(-4.9)} \\ t_{1,2}=\frac{-4\pm\sqrt[]{212}}{-9.8} \\ t_1\approx\frac{-4+14.56}{-9.8}\approx-1.08 \\ t_2\approx\frac{-4-14.56}{-9.8}\approx1.89 \end{gathered}$

Given that variable t measures time it cannot be negative, then the result t = -1.08 is discarded.

The diver enters the water after 1.89 seconds