Question

A formula that involves a small toy rocket and how long it will take to hit the ground

Answer 1

Given:

The height of the rocket after t second taking off is given by the formula,

`h=-2t^2+2t+12`

Required:

We need to find the time when the rocket hit the ground.

Step-by-step explanation:

We know that the greatest height is zero when the rocket hit the ground.

Substitute h =0 in the given equation to find the time when the rocket hit the ground.

`-2t^2+2t+12=0`

Divide both sides of the equation by (-2).

`-(2t^2)/(-2)+(2t)/(-2)+(12)/(-2)=(0)/(-2)`
`t^2-t-6=0`
`Use\text{ }-t=-3t+2t.`

`t^2-3t+2t-6=0`

Taking out the common term.

`t(t-3)+2(t-3)=0`

`(t-3)(t+2)=0`

`(t-3)=0,(t+2)=0`
`t=3\text{ or t=-2.}`

The time should not be of negative value.

`t=3`