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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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Write a quadratic equation ...

 

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.

laugh  !

 May 2, 2022
edited by asinus  May 2, 2022

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