1. Car X is a 2600-kg car traveling at 35 m/s. It collides with Car Y, a 1450-kg car moving 12 m/s in the same direction. The two cars stick together upon colliding. What is the new speed of these cars? 2. A 42.0-g bullet leaves a rifle and embeds itself in a 2.96-kg stationary block of wood. The wood-bullet combination flies away with a velocity of 4.9 m/s. What was the initial velocity of the bullet in m/s?

3. Ball A is 0.40 kg and it collides with Ball B of mass 0.60 kg. Ball A initially moves to the right with a velocity of 1.0 m/s while Ball B moves to the left at 2.0 m/s (or -2.0 m/s). After the collision, Ball A moves to the left at 2.60 m/s. What is the velocity of Ball B in m/s?

(a) the velocity of the plank relative to the frozen pond is 0.825 m/s

(b) the velocity of the plank relative to the frozen pond is 0.275 m/s

Explanation:

Given information:

student's mass, = 50kg

wooden plank's mass, = 150 kg

Note : all the velocity is in vector

student's velocity relative to the plank, = 1.10i m/s

student's velocity relative to frozen pond,

= +

(a) the velocity of the plank relative to the frozen pond,

to calculate the velocity of the plank relative to the frozen pond, we can start from the momentum, p.

The total momentum is

p = +

is the velocity of student relative to the frozen pond

is the velocity of the plank relative to the frozen pond

at rest on a frozen pond, the momentum is 0. so,

p = 0

+ = 0

= -

*the negative indicates that the student and the plank are moving in opposite direction

now subtitute student's velocity relative to frozen pond, to the equation.

= -

= -

- ) =  -

- = -

= -

= -

= -0.825 i m/s

the velocity of the plank relative to the frozen pond is 0.825 m/s in the opposite direction

(b) the velocity of the student relative to the frozen pond

= +

= (1.10i m/s) + (- 0.825i m/s)

= (1.10i m/s - 0.825i m/s)

= 0.275i m/s

the velocity of the plank relative to the frozen pond is 0.275 m/s.