A ball with a mass of # 5 kg# is rolling at #18 m/s# and elastically collides with a resting ball with a mass of #3 kg#. What are the post-collision velocities of the balls?

Answer 1

Given

Mass of 1st ball #m_1=5# kg
Mass of 2nd ball #m_2=3# kg
Initial velocity of 1st ball #u_1=18m"/"s#
Initial velocity of 2nd ball #u_2=0m"/"s#
Let post collision velocity of 1st ball be #v_1# and that of 2nd ball be #v_2#

By conservation of momentum

#m_1u_1+m_2u_2=m_1v_1+m_2v_2#
#5*18+3*0=5v_1+3v_2#
#=>5v_1+3v_2=90.....[1]#

Again the collision being elastic one the relative velocity of one ball with respect to the other is reversed by the collision and we get

#v_2-v_1=u_1-u_2#
#=>v_2-v_1=18-0#
#=>v_2-v_1=18.......[2]#

By [1] and [2] we get

#5v_1+3(18+v_1)=90#
#=>8v_1=90-54=36#
#=>v_1=36/8=4.5# m/s
#v_2=18+v_1=18+4.5=22.5#m/s
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

(v_1 = \frac{m_1 - m_2}{m_1 + m_2} \cdot u_1 + \frac{2m_2}{m_1 + m_2} \cdot u_2)

(v_2 = \frac{2m_1}{m_1 + m_2} \cdot u_1 + \frac{m_2 - m_1}{m_1 + m_2} \cdot u_2)

Substitute the values:

(v_1 = \frac{5 - 3}{5 + 3} \cdot 18 + \frac{2 \cdot 3}{5 + 3} \cdot 0)

(v_2 = \frac{2 \cdot 5}{5 + 3} \cdot 18 + \frac{3 - 5}{5 + 3} \cdot 0)

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7