Question

Identical twins, each with mass 51 kg, are on ice skates and at rest on a frozen lake, which may be taken as frictionless. Twin A is carrying a backpack and she throws it horizontally at 2.6 m/s to Twin B. After throwing the backpack, twin A gains a velocity of 1.3.

Neglecting any gravity effects, what are the subsequent speeds of Twin B in m/s.

Answer 1

Here we have given that,

dentical twins, each with mass mA = mB = 51 kg,

Twin A is carrying a backpack and she throws it horizontally at 2.6 m/s to Twin B.

After throwing the backpack, twin A gains a velocity of 1.3 m/s

Here initially they both are at rest so that,

Vi = 0 m/s

Using conservation of linear momentum we will have,

MAVA + M2V2 = MAV1' + M2V2'

On plugging the values we will get,

0 + M2 ×0 = 51 × -1.3 + M2 × 2.6

M2 = mass of bagpack = 51×1.3/2.6 = 25.5 kg

Now

When twin B receive a bag then again here we can use conservation of linear momentum as,

MBVB + M2V2 = MBVB' + M2V2'

as initial twin B is as rest so that and after catching the bagpack they have combined mass as MB2 so thatwe will have new equation as

0 + 25.5 ×2.6 = (M2 + MB) × VB'

VB' = 66.3/76.5 = 0.8666666667 m/s

Hence, the subsequent speeds of Twin B is 0.8667 m/s