Question

Two 7.5 kg bodies, A and B, collide. The velocities before the collision are v Overscript right-arrow EndScripts Subscript Upper A Baseline equals left-parenthesis 40 i Overscript ̂ EndScripts plus 49 j Overscript ̂ EndScripts right-parenthesis m divided by s and v Overscript right-arrow EndScripts Subscript Upper B Baseline equals left-parenthesis 35 i Overscript ̂ EndScripts plus 11 j Overscript ̂ EndScripts right-parenthesis m divided by s. After the collision, v Overscript right-arrow EndScripts Subscript Upper A Superscript prime Baseline equals left-parenthesis 14 i Overscript ̂ EndScripts plus 21 j Overscript ̂ EndScripts right-parenthesis m divided by s. What are (a) the x-component and (b) the y-component of the final velocity of B? (c) What is the change in the total kinetic energy (including sign)?

Two 7.5 kg bodies, A and B, collide. The velocities before the collision are V A I40i 49 j S and v8 35i 11 j m/s After the collision v A 14i 21 j m/s What are (a) the x-component and (b) the y-component of the final velocity of B? (c) What is the change in the total kinetic energy (including sign)? (a) Number Units (b) Number Units (c) Number Units

Answer 1

Here momentum is conserved in x and y direction

in x-direction

mA*VAxi + mB*VBxi = mA*VAxf + mB*VBxf

VBxf = (mA*VAxi + mB*VBxi - mA*VAxf)/mB

here mA = mB

VBxf = (VAxi + VBxi - VAxf)

= 40 + 35 - 14

= 61 m/s

in x-direction

mA*VAyi + mB*VByi = mA*VAyf + mB*VByf

VByf = (mA*VAyi + mB*VByi - mA*VAyf)/mB

here mA = mB

VByf = (VAyi + VByi - VAyf)

= 49 + 11 - 21

= 39 m/s

Ki = 0.5*mA*(VAxi^2 + VAyi^2) + 0.5*mB*(VBxi^2 + VByi^2)

= 0.5*7.5*(40^2 + 49^2) + 0.5*7.5*(35^2 + 11^2)

= 20051.25 J

Kf = 0.5*mA*(VAxf^2 + VAyf^2) + 0.5*mB*(VBxf^2 + VByf^2)

= 0.5*7.5*(14^2 + 21^2) + 0.5*7.5*(61^2 + 39^2)

= 22046.25 J

kf - ki = 22046.25-20051.25 = 1995 J