[lindley]

A shell is shot with an initial velocity of v of 20m/s at an angle of teta = 60 with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed immediately after the explosion is zero, falls vertically. How far from the gun does the other fragment land, assuming that the terrain is level and that air drag is negligible?

p/s: i tried solving is using the projectile motion way but i couldnt get the answer. this question is under the subtopic of " Newtons 2nd law for a system of particles". answer is 53m btw.

can anyone help me solve this question by today plsssss?????

[phalken]

First find the time required to reach the top of the trajectory. Split the velocity into the sine and cosine components. So vertically, you know the final velocity Vf = 0 then.

Vf = V0 + at
0 = 20sin(60) - 9.81t
t = 1.766sec

Then there's a horizontal velocity change, because of conservation of momentum. Let original mass = 2M

(2M)(20cos60) = M(V2)
V2 = 20 m/s

The time required for the object to fall down is the same as it takes to go up, since there was no change in the vertical frame.

So the total distance traveled would be the first horizontal speed x time to go up, plus the second horizontal speed x time to come down.
10(1.766) + 20(1.766) = 53m

[lindley]

O.o your method works too! lol thanks! Is there another method to use, say by using the distance of centre of mass?

[phalken]

Usually you only use the center of mass frame if after exploding, both parts of the mass has different speeds. Then the equations get messy because you have to use momentum AND kinetic energy to solve for the two velocities.

In this case, using center of mass frame is a waste of time =/ The conversions are really not worth it unless it's, like I said above, when the two parts have different velocities.

And you're welcome =)

[wolfwolf]

just a quick question. can someone give me advice on how to do well in my intro to biology open note exam? he let us use our notes on tests, but its only one hour. i did really bad on the first exam, now i'm kinda scare for this next one. any tips? thx.