Find velocity given y and angle

[mandy9008]

Homework Statement

Tarzan swings on a 34.0 m long vine initially inclined at an angle of 38.0° with the vertical.
(a) What is his speed at the bottom of the swing if he starts from rest?
(b) What is his speed at the bottom of the swing if he pushes off with a speed of 2.00 m/s?

The Attempt at a Solution

I honestly do not even know where to begin.

 

[wwshr87]

Use conservation of energy, you know the height at which he starts, you know the height at the bottom of the swing. You know the initial speed for both cases. This should get you started. KEi + PEi = KEf + PEf

 

[inky]

Homework Statement

Tarzan swings on a 34.0 m long vine initially inclined at an angle of 38.0° with the vertical.
(a) What is his speed at the bottom of the swing if he starts from rest?
(b) What is his speed at the bottom of the swing if he pushes off with a speed of 2.00 m/s?

The Attempt at a Solution

I honestly do not even know where to begin.

(1)Firstly draw freebody diagram. Consider how many forces acting on Tarzan.
(2) Use Newton's Second law then find acceleration.
(3) Find the length between tarzan initial and final condition.
(4) Find the velocity at the bottom.

 

[mandy9008]

KE + PE = KE + PE
mgh = 1/2 mv²
v² = gh/2
v² = (9.8 m/s²)(34m) / 2
v= 12.91 m/s

where does the angle come into play?
when i entered this answer, it told me that I was within 10% of the correct answer

 

[wwshr87]

See figure attached.

 

[joshmdmd]

basically find the change in height using trig... the length of the vine * cos(angle)

then you take the length and subtract what you found..
next find (mass)(9.81)(change in height)

equate that to 1/2mv^2

so take the answer, multiply by 2, divide by mass and then get the squareroot..

thats the velocity..

all this is is mgh=1/2mv^2 (Eg=Ek)

 

[mandy9008]

I don't know the mass though

 

[wwshr87]

mandy, if you write out KEi + PEi = KEf + PEf, you will notice a common term which can be canceled.

 

[joshmdmd]

i just did the question.. ill post the solution.. scanning it atm..

mass cancels out.. are the answers 16 and 16.1m/s?

 

[mandy9008]

I did cancel out the mass when I solved this equation. Is this not the correct equation?

KE + PE = KE + PE
mgh = 1/2 mv²
v² = gh/2
v² = (9.8 m/s²)(34m) / 2
v= 12.91 m/s

 

[joshmdmd]

its not bc you're dividing by 2 when you should be multiplying.. you're also ignoring the angle and delta heighthttp://yfrog.com/6bscan0001yj

 

[joshmdmd]

http://img227.imageshack.us/img227/5659/scan0001y.jpg

this is my solution..

 

[wwshr87]

The equation is correct, and you canceled out the mass, but the height is not correct. Instead use delta h in the figure which i attached. Tarzan did not release from 0 degrees, therefore take this into account.

 

[wwshr87]

joshmdmd, you must be rather careful here. If the 38 degrees are measured from the x-axis like I have drawn then in order to obtain the y-component you must take the sine of the angle.

 

[joshmdmd]

your eq'n should be v^2=2gh

 

[joshmdmd]

joshmdmd, you must be rather careful here. If the 38 degrees are measured from the x-axis like I have drawn then in order to obtain the y-component you must take the sine of the angle.

mmm

careful?

cos(90-38) = sin38

 

[joshmdmd]

mmm

careful?

cos(90-38) = sin38

oops.. i took theta in your drawing as 38.. =] you messed me up

 

[wwshr87]

Sorry for the confusion, just making sure you know what's going on.

 

[joshmdmd]

here we go.. corrections to answer..

v=(SQRT)2gh
v=11.886m/s

b)
v=12.22

 

[mandy9008]

Josh, the answer in your scan is wrong. When i did it and got 12.91 m, it said that I was within 10% of the correct answer.

 

[joshmdmd]

Sorry for the confusion, just making sure you know what's going on.

its okay.
wasnt paying attn to the diagram .. as you can see i ripped yours in mine.

 

[joshmdmd]

Josh, the answer in your scan is wrong. When i did it and got 12.91 m, it said that I was within 10% of the correct answer.

read the second page =]

 

[wwshr87]

Are you guys doing mastering physics?

 

[joshmdmd]

Are you guys doing mastering physics?

if you mean uni for phys.. ima go to uft or waterloo for aerospace engineering/mechanical engineering.. I am currently gr 11.. writing gr 12 phys exam on friday.

 

[wwshr87]

joshmdmd, alright good luck. You seem to be on the right track by taking physics in high school.

 

[mandy9008]

Correct! :)

 

[joshmdmd]

joshmdmd, alright good luck. You seem to be on the right track by taking physics in high school.

thanks man, you mastering atm?

all the people in my class think ima idiot bc I am doing 11/12 phys this year and 11/12 chem next year.. lol.. they say ill forget phys before uni

 

[wwshr87]

I am about to begin a master's in electrical engineering. I think you are doing great you'll never totally forget this things.

 

[joshmdmd]

I am about to begin a master's in electrical engineering. I think you are doing great you'll never totally forget this things.

that means a lot bro.. have fun and enjoy yourself... schools always funner than work =]

 

[joshmdmd]

btw go back to mandys other question and see if you can add on to what I did..

https://www.physicsforums.com/showthread.php?t=411806