Question

When joey dives off a diving board, the equation of his pathway can be modeled by h=-16tsquared+15t+12. Find joeys maximum height and the time it will take for joey to reach the water

Answer 1

Answer with explanation:

Given : When joey dives off a diving board, the equation of his pathway can be modeled by $h=-16t^2+15t+12$ .

We use vertex formula $x=\dfrac{-b}{2a}$ to find the maximum height of quadratic polynomial $ax^2+bx+c$. (i)

As compare the given polynomial to (i), we have

a=-16 and b= 15

Then , the maximum height = $\dfrac{-(15)}{2(-16)}=\dfrac{15}{32}=0.46875$

Hence, the maximum height is 0.46875 m.

When Joey reaches the water then h= 0

i.e. $0=-16t^2+15t+12$

$16t^2-15t-12=0\\\\ t=\dfrac{-(-15)\pm\sqrt{(-15)^2-4(16)(-12)}}{2(16)}\\\\=\dfrac{15\pm\sqrt{225+768}}{32}=\dfrac{15\pm\sqrt{993} }{32}=\dfrac{15\pm31.512}{32}\\\\t=\dfrac{15-31.512}{32}\ \ or\ \ t=\dfrac{15+31.512}{32}\\\\t=-0.516\ or \ t=1.4535\approx1.45\\\\\Rightarrow\ t=1.45\ \ \ [\text{Time cannot be negative}]$

Hence, the time it will take for Joey to reach the water is 1.45 seconds.