Question

Hello! I need help with a practice problem for my math class. It involves “solving a word problem using a quadratic equation with irrational roots”. Thank you so much. I will include a picture of the problem.

Answer 1

$t_1=9.36,t_2=0.64$

1) Note that according to this equation the rocket describes a parabola when it is flying.

2) We need to know then at what instant of time the rocket is at 30 meters. So we can write out the following:

$\begin{gathered} 30=50t-5t^2 \\ 5t^2-50t+30=0 \\ (\div5)5t^2-50t+30=0(\div5) \\ t^2-10t+6=0 \\ t=\frac{10\pm\sqrt[]{(-10)^2-4(1)(6)}}{2(1)} \\ t_1=5+\sqrt[]{19},t_2=5-\sqrt[]{19} \\ t_1=9.36,t_2=0.64 \end{gathered}$

3) Thus the rocket will be at 30 meters high in 0.64 seconds and in 9.35 seconds