Question

A monkey of mass 20kg rides on a 40kg
trolley moving with constant speed of 8m/s
along a horizontal track. If the monkey jumps
vertically to grab the overhanging branch of a
tree, the speed of the trolley after the
monkey has jumped off is -​

Answer 1

$\large \sf\underline{ \underline{ \red{given : }}}$

• Mass of monkey (m1) = 20kg

• Mass of trolly (m2) = 40kg

• Initial speed of monkey (u1) = 8m/sec

• Inital speed of trolly (u2) = 8m/sec

• Final speed of monkey (v1) = 0m/sec

$\\ \\ \large \sf\underline{ \underline{ \red{to \: find : }}}$

• Final speed of trolly (v2)

$\\ \\ \large \sf\underline{ \underline{ \red{approach : }}}$

• Momentum is conserved as no external force is applied.

$\\ \therefore \boxed{ \tt{m1u1 + m2u2 = m1v1 + m2v2}}$

$\\ \large \sf\underline{ \underline{ \red{solution : }}}$

We have all values ,

Putting values , we get..

$\\ \tt{20(8) + 40(8) = 20(0) + 40(v2)} \\ \\ \\ \tt{160 + 320 = 0 + 40(v2)} \\ \\ \\ \tt{480 = 40(v2)} \\ \\ \\ \tt{v2 = \frac{ \cancel{480}}{ \cancel{40} }} \\ \\ \\ \boxed{\therefore \tt{ \pink{v2 = 12 \: \frac{m}{sec} }} }$

Hence , speed of trolly after monkey jumps is 12m/sec.