Collision in Midair: Find Speed After Impact

[roam]

Homework Statement

If one bullet of mass 5 g that was moving to the right at speed 250 m/s at 20° above the horizontal collieded and fused with a 3 g bullet traveling to the left at speed 280 m/s at 15° above the horizontal, then what is their speed after impact?

The Attempt at a Solution

For the bullet of mass 5g

$$v_{xi}= 250 cos 20 = 234.9$$

For the bullet of mass 5g

$$v_{xi}= 280 cos 15 = 270.4$$

Since the question says "what is their speed after impact", I guess it means the collision is perfectly inelastic and they both stick together and travel to the same direction. In this case the EK before & after is not equal but momentum is conserved

Taking motion to the right as positive.

mv_1ix+mv_2ix =MV_f

$$\frac{3}{1000} 270.4 + \frac{5}{1000} \times -234.9= \frac{3+5}{1000}v_f$$

But when I solve for v_f this doesn't produce the right answer. The correct answer has to be 93 m/s. Could anyone help me please?

 

[pat666]

You forgot to take into account the j movement here's what you should have done

V1=250cos20i+250sin20j
v2=-280cos15i+280sin15j you were taking left as negative

then
(250cos20i+250sin20j)*5+(-280cos15i+280sin15j)3=(3+5)v
1174.62i+427.525j+-811.378i+217.408j=8v
group i and j
363.328i+644.933j=8v
v=45.4048i+80.6166j
take the magnitude
v=sqrt(45.4048^2+80.6166^2)
v=92.5m/s or 93 m/s
they will often ask for an angle in this type of question which is just
tan^-1(80.6166/45.4048)Let me know if this was helpful please...

ps as long as your mass is in constant units there is no need to change it to si units...

 

[roam]

You forgot to take into account the j movement here's what you should have done

V1=250cos20i+250sin20j
v2=-280cos15i+280sin15j you were taking left as negative

then
(250cos20i+250sin20j)*5+(-280cos15i+280sin15j)3=(3+5)v
1174.62i+427.525j+-811.378i+217.408j=8v
group i and j
363.328i+644.933j=8v
v=45.4048i+80.6166j
take the magnitude
v=sqrt(45.4048^2+80.6166^2)
v=92.5m/s or 93 m/s



they will often ask for an angle in this type of question which is just
tan^-1(80.6166/45.4048)


Let me know if this was helpful please...




ps as long as your mass is in constant units there is no need to change it to si units...

Very helpful! Thank you so much! I had completely forgotten about the vertical $$\hat{j}$$ direction. But could you please explain a little bit more on why you didn't change g into kg for the masses. I didn't quite understand what you meant by "constant units"...

 

[pat666]

That divide by 1000 to convert from grams to kg will come out because its on both sides, you can leave it in if you want it will give you exactly the same answer.. your best bet in high school is to just change every thing to si units that way you can't go wrong.