Two fun-loving otters are sliding toward each other on a muddy (and hence frictionless) horizontal surface. One of them, of mass 8.50 kg, is sliding to the left at 6.00 m/s, while the other, of mass 5.75 kg, is slipping to the right at 5.50 m/s. They hold fast to each other after they collide.

(a) Find the magnitude and direction of the velocity of these free-spirited otters right after they collide.
(b) How much mechanical energy dissipates during this play?

(a). The magnitude and direction of the velocity of the otters after collision is 1.35 m/s toward left.

(b). The mechanical energy dissipates during this play is 226.98 J.

Explanation:

Given that,

Mass of one otter = 8.50 kg

Speed = 6.00 m/s

Mass of other = 5.75 kg

Speed = 5.50 m/s

(a). We need to calculate the magnitude and direction of the velocity of these free-spirited otters right after they collide

Using conservation of momentum

Put the value into the formula

Negative sign shows the direction of motion of the object after collision is toward left.

(b). We need to calculate the initial kinetic energy

Using formula of kinetic energy

Put the value into the formula

We need to calculate the final kinetic energy

Using formula of kinetic energy

Put the value into the formula

We need to calculate the mechanical energy dissipates during this play

Using formula of loss of mechanical energy

Put the value into the formula

Negative sign shows the loss of mechanical energy

Hence, (a). The magnitude and direction of the velocity of the otters after collision is 1.35 m/s toward left.

(b). The mechanical energy dissipates during this play is 226.98 J.