Question

Really need help please Quadratic Equation?

A model rocket is launched with an initial upward velocity of 30 m/s. The rockets height h ( in meters) after t seconds is givenby the following.
h=30t-5t^2
Find all values of t for which the rockets height is 10 meters.
Round your answers to the nearest hundredth

Answer 1

t = 0.35, t = 5.65

Explanation:

You are given h = 30t - 5t^2. Put this in standard form order (ax^2 + bx + c) by switching the two terms.

h = -5t^2 + 30t

Now you want to find all the values of t for which the rocket's height is 10 meters, so your equation will be equal to 10 instead of h, because 10 is the height you are solving for.

10 = -5t^2 + 30t

Make the entire equation equal to 0 by subtracting 10 from both sides.

0 = -5t^2 + 30t - 10

To solve this quadratic equation, the easiest way would be to use the quadratic formula:
`(-b\pm√(b^2-4ac))/(2a)`

Identify your a, b, and c values in the standard form equation (a = -5, b = 30, c = -10) and substitute these values into the quadratic formula.
`(-(30)\pm√((30)^2-4(-5)(-10)) )/(2(-5)) \rightarrow (-30\pm√(900-200=700) )/(-10) \rightarrow (-30\pm√(700) )/(-10)`

We have (-30 ± sqrt 700)/-10.

Use a calculator to input the two solutions and solve for them; (-30 + sqrt 700)/-10 and (-30 - sqrt 700)/-10.

`(-30+√(700) )/(-10) = 0.35`

`(-30- √(700) )/(-10) =5.65`