Katniss fires an arrow towards another tribute with a peed of 7.0 x 10^3 m/s. The arrow has a mass of 105 grams and the "dead" tribute has (had) a mass of 58 kg.
a. Assume that the arrow became lodged in the tribute; determine the velocity of the arrow tribute system.
b. Calculate the kinetic energy of arrow-tribute system

Question

Katniss fires an arrow towards another tribute with a peed of 7.0 x 10^3 m/s. The arrow has a mass of 105 grams and the "dead" tribute has (had) a mass of 58 kg.
a. Assume that the arrow became lodged in the tribute; determine the velocity of the arrow tribute system.
b. Calculate the kinetic energy of arrow-tribute system

anonymous · Answer

conservation of momentum:
total momentum before = total momentum after
$$m _{1}v _{1} + m _{2}v _{2} = m _{1}\prime v _{1}\prime + m _{2}\prime v _{2} \prime  $$

anonymous · Answer

m1=105g, m2=58kg 
v1=7.0x10^3m/s or is it 0

anonymous · Answer

For this question, momentum before is just 
0.105 x 7000
And after, the total momentum is 
(0.105 + 58) x velocity of both together

anonymous · Answer

sorry, you are right, and v1 is 7000, v2 = 0 (the tribute is not moving)

anonymous · Answer

just follow my method now, do you understand it ok?

anonymous · Answer

and v2' is still 0 rite?

anonymous · Answer

i got v1'= 7000m/s o.O

anonymous · Answer

thats my answer because we want to know v1' for part a.) rite? o:

anonymous · Answer

this question is a special case of that formula, as the two masses join, and have one velocity. Basically$$v _{1}\prime = v _{2}\prime $$so the right hand side can be simplified to:$$m _{1}\prime v _{1}\prime + m _{2}\prime v _{1}\prime  = (m _{1}\prime + m _{2}\prime  )v _{1}\prime  $$

anonymous · Answer

oh because the arrow stops right after it hits the tribute rite? o:

anonymous · Answer

so were looking for vf? o.O

anonymous · Answer

well, the arrow doesn't stop, it 'takes' the tribute with it. You could just say v1' = v2' = vf. my answer is 12.6 m/s for a)

anonymous · Answer

so i got 4,509.2

anonymous · Answer

:/  i think you may not be converting units, everything must be in kg, to get m/s
the equation is:
7000 x 0.105 = (58 + 0.105)vf
vf = (7000x0.105)/(58+0.105)

anonymous · Answer

ready for part b), or are you ok with that bit?

anonymous · Answer

its not .105 its 105 xD anyways thank you~ i got the same answer :DDD

anonymous · Answer

no i dont get part b.)

anonymous · Answer

KE=1/2mv^2?

anonymous · Answer

It is 0.105, 105g = 0.105kg
You must always convert units!

anonymous · Answer

perfect! But what will you put in for m, v?

anonymous · Answer

oh ok :)

anonymous · Answer

v=7000 and idk for m? xD

anonymous · Answer

remember questions are often scaffolded. This means that that you use something you just worked out in the next part. It wants the KE for the system. (the system we just worked out the velocity of!)
so v = 12.6 m/s
m = (m1 + m2)