suppose a rover landed on Jupiter and could launch a rock into the air. assume the function h(t)=-13^2+50t+2 models the rocks height above the surface,h, in meters after t seconds from release. what is the height of the rock at the time of release?

Question

suppose a rover landed on Jupiter and could launch a rock into the air. assume the function h(t)=-13^2+50t+2 models the rocks height above the surface,h, in meters after t seconds from release.    what is the height of the rock at the time of release?

anonymous · Answer

Set t=0 and solve.

luigi0210 · Answer

It would be 2 meters, if you set it equal to 0..

anonymous · Answer

okay thanks. the next part of the question is, when will the rock reach its maximum height ?

anonymous · Answer

Assuming, of course, that the 13^2 is supposed to mean 13 t^2.

anonymous · Answer

yes sorry 13t^2

anonymous · Answer

Maximum height is most easily found by taking the derivative and setting it equal to zero. Solve for t and you have your time, and reinsert that t in the original equation for the height.

anonymous · Answer

am i using the quadratic equation by setting t to 0?

luigi0210 · Answer

You could graph it too, if you haven't learned derivatives

anonymous · Answer

No, that'd get you the time when h=0. The derivative of quadratics at^2+bt+c is 2at+b, but I think there was an elaborate equation to find h without that...

agent0smith · Answer

There's no need for calculus or graphs. Just find the vertex of the parabola from $$\Large x= -\frac{ b }{ 2a }$$ (though that ^ is derived with calculus)

Then plug x back into the h equation.

agent0smith · Answer

Since it's t, $$\Large t= -\frac{ b }{ 2a }$$
a and b are from $$\large ax^2 +bx +c$$

anonymous · Answer

im getting a tad confused lol, i know there is a set of equations to solve this particular problem i just cant seem to remember them, there are 5 parts to this question : what is the height of the rock at the time of release, how high is the rock after one second, when will the rock reach its maximum height, what is the maximum height and when will the rock hit the surface. so you're saying that to find the height at time of release  i should use the equation -b/2a?

agent0smith · Answer

when will the rock reach its maximum height

when t=-b/2a

anonymous · Answer

Height at time of release is just H(0). H(1) gives height at one second. Max height is given by t=-b/2a. H(t) with that t gives the height itself. The rock hits the surface, assuming the surface is at height 0, when H(t) =-13t^2+50t+2 0 (use a quadratic here, and remember that negative times tell you when the rock would have been launched if it were to be in the same place with the same velocity as this rock but are otherwise nonsensical)

anonymous · Answer

okay thank you ! i'll go try those out now.

anonymous · Answer

hi again lol, so i got 3.88 seconds for when the rock will hit the planets surface, does that make sense to you all ? if so i did it right

agent0smith · Answer

Looks about right. You can check your values from a graph... https://www.google.com/search?q=-13t%5E2%2B50t%2B2&aq=f&oq=-13t%5E2%2B50t%2B2&aqs=chrome.0.57.1729j0&sourceid=chrome&ie=UTF-8