Derivative problem

1. Feb 3, 2008

Flappy

1. The problem statement, all variables and given/known data
"If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters) after t seconds is given by H = 10t - 1.86t^2."

a) Find the velocity of the rock when t = a
b) Find the velocity of the rock after 1 second
c) When will the rock hit the surface?
d) With what velocity will the rock hit the surface?

3. The attempt at a solution

I was able to do parts a and b. Im stuck at c and d though.

For (a) I derived the formula that is given.
Which turns to: 10 - 3.72a
For (b) I substituted 1 into the equation which gives: 6.28

Now how would I go about finding out when the rock will hit the surface and it's velocity? Any help appreciated.

2. Feb 3, 2008

i2837856393

your velocity is the derivative.... v= 10-3.72t

there are going to be 2 times when the rock is on the ground.
one at time zero and one at the 2nd time... which is 10/1.86t

1.86t2-10t=0
1.86t=10
t=0 and t= (about) 5.37

to find the velocity

you plug in 5.37 into the derivative:

v= 10-3.72t
= 10-3.72(5.37)= -9.9764

which equals... negative 10
as we can see, it was thrown up at 10 m/s and coming down it should be the opposite of that... -10.

:) enjoy!

need any more explanations?