Physics Word Problem: Arrow and moving target collision

[phantom lancer]

Homework Statement

Find the 2 unknown variables.[/B]

Homework Equations

Am I doing this right? Can someone help me find the solution?[/B]

The Attempt at a Solution

To compute for the velocity of the target/arrow combination immediately after the collision:
M_bV_{bi}=M_bV_{bf}+M_wV_{wf}
M_bV_{bf}=M_bV_{bf}-M_w-M_wV_{wf}
V_{bf}=\frac M_bV_{bi}-M_wV_{wf} M_b
V_{af}=\frac M_aV_{ai}-M_tV_{tf} M_a
V_{af}=\frac M_aV_{ai}-M_i M_a

V_{af}=\frac (0.323)(23 m/s)+(0.52 kg) (0.323 kg)
V_{af)=26.6 m/s down

To compute for velocity of the target/arrow combination just before it strikes the ground.

v=6.5 m/s - (9.8 m/s^2)[/B]

 

[kuruman]

Can you explain a little better what you have done? The lack of proper LaTeX coding and the symbols that you use make your strategy hard to discern. Clearly you are attempting to conserve momentum through the collision, but I see no calculation of the target's speed just before the collision. What is the meaning of 23 m/s? It cannot be the speed of the target because it has to be less than 15 m/s and it cannot be the speed of the arrow because it is given as 25 m/s. Also, the last equation seems to subtract an acceleration from a velocity. That cannot be.

 

[haruspex]

I inserted double hashes (#) to turn on the LaTeX engine, and some {} braces as necessary, but could not make sense of the last line.
The second line is also clearly wrong.

$M_bV_{bi}=M_bV_{bf}+M_wV_{wf}$
$M_bV_{bf}=M_bV_{bf}-M_w-M_wV_{wf}$
$V_{bf}=\frac {M_bV_{bi}-M_wV_{wf}}{ M_b}$
$V_{af}=\frac {M_aV_{ai}-M_tV_{tf}} {M_a}$
V_{af}=\frac M_aV_{ai}-M_i M_a