ohohaye
  • ohohaye
At what time will the rocket hit the ground? Equation: h= -5t^2+30t+10 Please show me how to do this
Mathematics
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schrodinger
  • schrodinger
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whpalmer4
  • whpalmer4
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
  • ohohaye
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
  • ohohaye
@whpalmer4

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whpalmer4
  • whpalmer4
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
  • ohohaye
Oh ok

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