A ball with a mass of #7 kg # and velocity of #1 m/s# collides with a second ball with a mass of #2 kg# and velocity of #- 5 m/s#. If #75%# of the kinetic energy is lost, what are the final velocities of the balls?

Answer 1

#v_1=0.315\ m/s# & #v_2=-2.602\m/s# or
#v_1=-0.982\ m/s# & #v_2=1.937\m/s#

Let #u_1=1 m/s# & #u_2=-5 m/s# be the initial velocities of two balls having masses #m_1=7\ kg\ # & #\m_2=2\ kg# moving in opposite directions i.e. first one is moving in +ve x-direction & other in -ve x-direction, After collision let #v_1# & #v_2# be the velocities of balls in +ve x-direction
By law of conservation of momentum in +ve x-direction, we have #m_1u_1+m_2u_2=m_1v_1+m_2v_2#
#7(1)+2(-5)=7v_1+2v_2#
#7v_1+2v_2=-3\ .......(1)#
Now, loss of kinetic energy is #75%# hence
#(1-\frac{75}{100})(\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2)=(\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2)#
#1/4(\frac{1}{2}7(1)^2+\frac{1}{2}2(5)^2)=\frac{1}{2}7v_1^2+\frac{1}{2}2v_2^2#
#28v_1^2+8v_2^2=57 \ ......(2)#
substituting the value of #v_2=\frac{-7v_1-3}{2}# from (1) into (2) as follows
#28v_1^2+8(\frac{-7v_1-3}{2})^2=57#
#42v_1^2+28v_1-13=0#
solving above quadratic equation, we get #v_1=0.315, -0.982# & corresponding value of #v_2=-2.602, 1.937#
Hence, the final velocities of both the balls are either #v_1=0.315\ m/s# & #v_2=-2.602\m/s#
or #v_1=-0.982\ m/s# & #v_2=1.937\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

The final velocity of the first ball is ( -2.4 , \text{m/s} ), and the final velocity of the second ball is ( -0.4 , \text{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 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