Two fun-loving otters are sliding toward each other on a muddy (and hence frictionless) horizontal surface. One of them, of mass 8.00 kg , is sliding to the left at 5.50 m/s , while the other, of mass 5.65 kg , is slipping to the right at 5.50 m/s . They hold fast to each other after they collide. Part A Find the magnitude of the velocity of these free-spirited otters right after they collide.

Explanation:

Applying the law of collision:

Sum of momentum before collision = sum of momentum after collision

Both object move with the same velocity after collision

Momentum = mass × velocity

Sum of momentum before collision;

= 5.65(5.4)+(8)(-5.5)

= 30.51-44

= -13.49kgm/s

Sum of momentum after collision

= (8.0+5.65)v

= 13.65v

Equate;

-13.49 = 13.65v

v = -13.49/13.65

v = -0.988m/s

Hence the velocity of the otter after collision is 0.988m/s ( both moving towards the left)

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day