Question

the height of a ball t seconds after it is thrown is modeled by the function h(t)=-4.9t^2 +15t+ 3, where h is the height of the ball in meters. Find the maximum height reached by the ball.

Answer 1

`(1419)/(98)` or 14.48 m (2 d.p )

Explanation:

1. There are 2 main ways to calculate this, either graphically or using an equation for the purpose of this question the equation is more useful. The equation to find where t is at its maximum value is:

`t = (-b)/(2a)`

2. Using this equation we get

`(-15)/(-9.8)` or 1.53 (2 d.p.)

so t is the greatest at
`(15)/(9.8)` (as both numbers being a negative divided by each other makes it a positive and also makes sense as time cannot be negative)

3. inputting the t value into the equation

h(
`(15)/(9.8)` ) = -4.9(
`(15)/(9.8)` )^2 + 15(
`(15)/(9.8)` ) + 3 =

-
`(1125)/(98)` +
`(1125)/(49)` +3 =

`(1419)/(98)` or 14.48 m (2 d.p )