an engineer is planning a firework show. he knows that the firework must reach a minimum height of 240m for…

Explanation:

Step1: Use kinematic - energy conservation

The initial kinetic energy $K_{i}=\frac{1}{2}mv_{0}^{2}$ and at the maximum - height, the final kinetic energy $K_{f} = 0$ and the potential energy $U_{f}=mgh$. By conservation of mechanical energy $K_{i}=U_{f}$, so $\frac{1}{2}mv_{0}^{2}=mgh$.

Step2: Solve for the initial velocity $v_{0}$

Canceling out the mass $m$ from both sides of the equation $\frac{1}{2}v_{0}^{2}=gh$. We know that $g = 9.8m/s^{2}$ and $h = 240m$. Then $v_{0}=\sqrt{2gh}$. $v_{0}=\sqrt{2\times9.8\times240}=\sqrt{4704}\approx68.6m/s$.

Step3: Convert $m/s$ to $mph$

We know that $1m/s = 2.23694mph$. So $v_{0}=68.6\times2.23694\approx153.5mph$.

Answer:

153.5 mph