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The equation y = -16t^2 + 60t described the height (in feet) of a projectile launched from the ground at 60 feet per second upward.  In how many seconds will the projectile first reach $$30$$ feet in height?  Express your answer as a decimal rounded to the nearest hundredth.

May 17, 2022

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The amount of time that would have passed once the ball reached 30 feet can be written by subsituting 30 in for y.

This gives: $$30 = -16t^2 + 60t$$. Subtracting 30 from both sides gives us this quadratic: $$0 = -16t^2 + 60t - 30$$

We can solve for t using the quadratic formula, which is $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$, because the quadratic is in the form $$0 = ax^2 + bx + c$$

Can you take it from here?

May 17, 2022