What is the Maximum Height of a Vertically Thrown Rock?

[jojo711]

Homework Statement

Brad tosses a rock straight up at 40.0 m/s. What is the rock's velocity after 1.8 seconds? (answer 22.36 m/s)
What is the velocity of the rock from the question above after 5.2 seconds? (answer -10.96)
What is the maximum height of the rock from the question above?

Homework Equations

V=Vo+at
X=Xo+Vot+1/2at^2
V^2=Vo^2+2a(X-Xo)

The Attempt at a Solution

I tried to find the maximum height for both times, but neither one was the right answer. I did the second equation (X=(40)(1.8)+1/2(-9.8)(3.24) and got 56.124 m and that wasn't right) then I tried the second equation with the second time (X=(40)(5.2)+1/2(-9.8)(27.04) and got the answer to be 75.504), but that wasn't right either. Please tell me what I am doing wrong!
*hint: the difference between the squares of the initial and final speeds is equal to twice the product of the acceleration due to gravity and the displacement.

 

[grzz]

how do you know that at max height the time is 1.8s?

 

[jiboom]

but the max height does not occur at 1.8 seconds or 5.2 seconds.
you don't know when the max height occurs,no do you care.
you only need to find the max height, so need distance traveled by rock to point when velocity is 0.
ie
u=40 v=0 (at top of motion) s=? a=-g

now use v^2=u^2+2AS

 

[jojo711]

I tried V^2=u^2+2AS (0^2)=(40^2)+2(-9.8)s and got 0 but I don't think that's the right answer.

 

[jiboom]

not sure how you get 0.?

you have 0=1600-19.6s

so s=0 certainly does not work

 

[grzz]

I tried V^2=u^2+2AS (0^2)=(40^2)+2(-9.8)s and got 0 but I don't think that's the right answer.

v$^{2}$ = u$^{2}$ + 2as

0 = 40$^{2}$ + 2(-9.8)s

s = 40$^{2}$/[2(-9.8)]

 

[jojo711]

Yes, but when you subtract 19.6 from 1600, you get 1580.4s and then don't you have to divide 0 by that number?

 

[jojo711]

v$^{2}$ = u$^{2}$ + 2as

0 = 40$^{2}$ + 2(-9.8)s

s = 40$^{2}$/[2(-9.8)]

I tried this and it gave me a negative number. (-81.63). It wasn't correct. I am so confused as to what to do!

 

[jiboom]

i am not going to solve

0=1600-19.6s

for you.

surely you can see if s was negative,-19.6s would be positive so you are adding two positives to get 0 which is absurd.

 

[grzz]

v$^{2}$ = u$^{2}$ + 2as

0 = 40$^{2}$ + 2(-9.8)s

Try to be LOGICAL.

0 = 1600 - 19.6s

Now add 19.6s to both sides:

19.6s = 1600 because 19.6s + (19.6s) = 0

Now divide both sides by 19.6:

s = 1600/19.6

s = ...

Of course you do not have to show my explanation in your solution. I only did that to show you how simple math is when you try your best to be LOGICAL.

 

[jojo711]

i got it, thank you for your help.