Basic Derivative Word Problem

[erix335]

Similar to my previous post, I've got another rates problem that seems to be a bit easier to solve:

If a stone is thrown vertically upward from the surface of the moon with an initial velocity of 10m/s, its height, in meters after t seconds is: h=10t-0.84t^2. What is the velocity of the stone after the stone rises to a height of 25 meters the first time?

So far I've taking h' and gotten h'=10-1.68t, then taken the height (25 meters) and plugged it in for h', giving me 1.5=-1.68t, showing the value of t to be 1.5/-1.68. Am I on the right track? Where do I take the problem from here?

 

[Deleted member 4993]

Similar to my previous post, I've got another rates problem that seems to be a bit easier to solve:

If a stone is thrown vertically upward from the surface of the moon with an initial velocity of 10m/s, its height, in meters after t seconds is: h=10t-0.84t^2. What is the velocity of the stone after the stone rises to a height of 25 meters the first time?

So far I've taking h' and gotten h'=10-1.68t, then taken the height (25 meters) and plugged it in for h', giving me 1.5=-1.68t, showing the value of t to be 1.5/-1.68. Am I on the right track? No

Where do I take the problem from here?

First calculate the time(t[sub:2xik2tm1]0[/sub:2xik2tm1]) it will take to reach the height of 25 meters - you will get two values for t[sub:2xik2tm1]O[/sub:2xik2tm1]

Then use these values of t[sub:2xik2tm1]O[/sub:2xik2tm1] in h' - to evaluate the velocity.

 

[mmm4444bot]

h = 10t - 0.84t^2

I've [found] … h' = 10 - 1.68t

This derivative is correct.


and plugged [h = 25] for h', giving me 1.5 = -1.68t

That's not correct at all. :shock: The symbols h and h' represent totally different things; you cannot substitute h for h'.

(By the way, 25 minus 10 does not equal 1.5)

Your mistake of substituting 25 feet for the speed of the rock concerns me. If you do not understand the difference between "height" and "velocity" (i.e., the meaning of symbols h and h', respectively), then you should review the meaning of a derivative before proceeding.

Otherwise, if that was just a silly mistake, then follow Subhotosh's guidance. I note that you do not need to evaluate h' for both values of time, only the first one.

Cheers