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# Algebra

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Write a quadratic equation that has the projectile reach a maximum height of 45 meters

May 2, 2022

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a maximum height of 45 meters.

Hello SBAHarper!

The launch velocity is  $$v_0.$$

The launch angle to the plane is $$\alpha.$$

Let the running time be t.

$${\color{blue}g}=9.805m/sec^2$$

$$h=-\frac{g}{2}\cdot t^2+v_0\cdot sin\ \alpha \cdot t\\ \dfrac{dh}{dt}=-g\cdot t+v_0\cdot sin\ \alpha=0\\ t=\dfrac{v_0\cdot sin\ \alpha}{g}$$

$$h_{max}=45m\\ =-\frac{g}{2}(\dfrac{v_0\cdot sin\ \alpha}{g})^2+v_0\cdot sin\ \alpha \cdot \dfrac{v_0\cdot sin\ \alpha}{g}\\ =-\dfrac{v_0^2\cdot sin^2\alpha}{2g}+\dfrac{2v_0^2\cdot sin^2\alpha}{2g}$$

$$h_{max}(=45m)=\dfrac{3}{2}\cdot \dfrac{v_0^2\cdot sin^2\alpha}{g}$$

Choose the angle of attack and calculate the launch speed

or

choose the launch speed and calculate the angle of attack.

!

May 2, 2022