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# algebra

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Write a quadratic equation that has the projectile being launched from 6 feet off the ground

May 2, 2022

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The general quadratic equation for a projectile's free fall is

$$p(t) = -at^2 + v_0t + h,$$

where $$a$$ represents acceleration due to gravity, $$v_0$$ is the initial (launch) velocity of the projectile, and $$h$$ is our starting height.

In terms of feet, the acceleration of a projectile due to gravity (on Earth) comes out to $$32.17 \frac{\text{ft}}{\text{s}^2}$$. I'll assume from your statement that there's no initial velocity present. Then, with a starting height of 6 feet, our quadratic equation will take the form

$$p(t) = -32.17t^2 +6.$$

May 2, 2022