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=(-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 =
`(-(15))/(2(-16))=(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=(-(-15)\pm√((-15)^2-4(16)(-12)))/(2(16))\\\\=(15\pm√(225+768))/(32)=(15\pm√(993) )/(32)=(15\pm31.512)/(32)\\\\t=(15-31.512)/(32)\ \ or\ \ t=(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.