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Luis, using appropriate safety precautions, fires a .22 caliber gun directly into the sky above him. The bullet travels at a speed of 1200 feet per second. The following equation gives the height of the bullet at any point in time:

H (height) = -16t2 + 1200t, where t is the number of seconds; t = 0 is the instant when the gun is fired.
How long will the bullet be in the air?

Respuesta :

MrRoyal

The equation represents height as a function of time.

The bullet was in the air for 75 seconds.

The equation is given as:

[tex]h(t) = -16t^2 + 1200t[/tex]

The time spent in the air is the time it takes the bullet to land on the ground.

When the bullet is on the ground, the height is:

[tex]h(t) = 0[/tex]

So, we have:

[tex]h(t) = -16t^2 + 1200t[/tex]

[tex]-16t^2 + 1200t = 0[/tex]

Factor out t

[tex]t(-16t + 1200) = 0[/tex]

Split

[tex]t = 0[/tex] or [tex]-16t + 1200 = 0[/tex]

[tex]t = 0[/tex] represents when the shot is fired.

So, we solve for t in [tex]-16t + 1200 = 0[/tex]

Collect like terms

[tex]16t = 1200[/tex]

Divide both sides by 16

[tex]t = 75[/tex]

Hence, the bullet was in the air for 75 seconds

Read more about height and time at:

https://brainly.com/question/2261757

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