Question

Identical twins, each with mass mt=53.5 kg, are on ice skates and at rest on a frozen lake, which may be taken as frictionless. Twin A is carrying a backpack of mass mbp=10.0 kg. She throws it horizontally at vbp=4.49 m/s to Twin B. Neglecting any gravity effects, find the resultant speed of Twin A (in m/s, and the sign matters!).

Answer 1

Using the law of conservation of momentum, we calculate that Twin A will move with a resultant speed of 0.84 m/s in the opposite direction to the thrown backpack.

Step-by-step explanation:

To find the resultant speed of Twin A after throwing the backpack to Twin B, we can use the law of conservation of momentum, which states that the total momentum of a closed system must remain constant if no external forces are acting on it. In this case, the lake is frictionless and no external horizontal forces are present. Since both twins and the backpack are initially at rest, the total initial momentum of the system is zero.

The momentum of the backpack after being thrown is mbp * vbp = 10.0 kg * 4.49 m/s = 44.9 kg*m/s, directed towards Twin B. To conserve momentum, Twin A must have an equal and opposite momentum, which we can denote as mt * vt = -44.9 kg*m/s, where vt is the velocity of Twin A. Solving for vt, we find that vt = -44.9 kg*m/s / 53.5 kg = -0.84 m/s. The negative sign indicates that Twin A's velocity is in the opposite direction to the backpack's throw.