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

A Formula That Involves A Small Toy Rocket And How Long It Will Take To Hit The Ground class=

Sagot :

Given:

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

[tex]h=-2t^2+2t+12[/tex]

Required:

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

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.

[tex]-2t^2+2t+12=0[/tex]

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

[tex]-\frac{2t^2}{-2}+\frac{2t}{-2}+\frac{12}{-2}=\frac{0}{-2}[/tex][tex]t^2-t-6=0[/tex][tex]Use\text{ }-t=-3t+2t.[/tex]

[tex]t^2-3t+2t-6=0[/tex]

Taking out the common term.

[tex]t(t-3)+2(t-3)=0[/tex]

[tex](t-3)(t+2)=0[/tex]

[tex](t-3)=0,(t+2)=0[/tex][tex]t=3\text{ or t=-2.}[/tex]

The time should not be of negative value.

[tex]t=3[/tex]

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