At what time will the rocket hit the ground?

Equation: h= -5t^2+30t+10

Please show me how to do this

Question

At what time will the rocket hit the ground?

Equation: h= -5t^2+30t+10

Please show me how to do this

whpalmer4 · Answer

Okay, $$h(t) = -5t^2+30t+10$$is the formula for the height of the rocket at time $t$.  You want to know when the rocket is back on the ground, or $h(t) = 0$.  So, you solve this equation:
$$0 = -5t^2 + 30t + 10$$for $t$ and ignore any answer that does not make sense (such as a value of $t < 0$).

ohohaye · Answer

What do you mean by this? "for t and ignore any answer that does not make sense (such as a value of t<0)."

ohohaye · Answer

@whpalmer4

whpalmer4 · Answer

Solve the equation for the value of $t$ that makes the height be 0.  It's a quadratic, so it has two solutions.  One of them in this case will be a negative number.  That means nothing in this scenario, because the rocket starts out at a height of 10 (the final term in the equation means the initial height is 10), but the parabola we use to model the height goes earlier than $t=0$.  Our model is only valid for $t \ge 0$, so we disregard the negative solution.

ohohaye · Answer

Oh ok