In an

$2$

$-$

D elastic collision between two bodies of mass m

$1$

$$and m

$2$

$,$

$$with m

$2$

$$initially at rest, mass

$1$

$$moves off at angle

$\backslash$

theta relative to the direction of its initial velocity and mass

$2$

$$at angle

$\backslash$

phi

$.$

$$An exam paper shows the equations below:

$$

$0$

$$m

$1$

v

$1$

i

$=$

$$m

$1$

v

$1$

f cos

$\backslash$

theta

$+$

$$m

$2$

v

$2$

f sin

$\backslash$

phi

$$

$=$

$$m

$1$

v

$1$

f sin

$\backslash$

theta

$+$

$$m

$2$

v

$2$

f cos

$\backslash$

phi

What error

$($

s

$)$

$$has the student made?

A

$.$

$$In the first equation, m

$2$

v

$2$

f sin

$\backslash$

phi should be m

$2$

v

$2$

f cos

$\backslash$

phi

$.$

B

$.$

$$In the second equation, m

$2$

v

$2$

f cos

$\backslash$

phi should be m

$2$

v

$2$

f sin

$\backslash$

phi

$.$

C

$.$

$$In the second equation, the plus sign between the terms on the right should be a minus sign

D

$.$

$$All of the errors listed above.

E

$.$

$$Only errors

$($

a

$)$

$$and

$($

b

$)$

$$above$.$