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# Algebra

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: Write a quadratic equation that has the projectile 5 feet off the ground after 1 second and then again after 4 seconds

May 2, 2022

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Hello SBAHarper!

$$v_0t\cdot sin\ \alpha-\frac{g}{2}t^2=h$$

The launch height is zero.

There are two unknowns to be determined:

Launch angle $$\alpha$$ and launch velocity $$v_0$$.

So two equations:

$$I.\ {\color{blue}v_0\cdot sin\ \alpha}\cdot 1sec-\frac{g}{2}\cdot (1sec)^2-5feet\cdot\frac{0.3048m}{feet}=0\\ II.\ {\color{blue}v_0\cdot sin\ \alpha}\cdot 4sec-\frac{g}{2}\cdot (4sec)^2-5feet\cdot\frac{0.3048m}{feet}=0\\ g=9,81m/s^2\\ I.\ v_0\cdot sin\ \alpha=\dfrac{6.429m}{1sec}\\ \color{blue}\alpha=arcsin\ \dfrac{6.429m}{v_0\cdot 1sec}$$

$$II.\ v_0\cdot sin\ \alpha\cdot 4sec-4.695m=0\\ \color{blue}\alpha=arcsin\ \dfrac{4.695m}{v_0\cdot 4sec}$$

These two functions do not intersect.

Ergo: The goal of 5ft after 1 second and 5ft after 4 seconds cannot be realized.

!

May 2, 2022
edited by asinus  May 2, 2022