Question

A 29.6 kg dog is running northward at 2.90 m/s , while a 7.70 kg cat is running eastward at 3.76 m/s . Their 76.7 kg owner has the same momentum as the two pets taken together. Find the direction and magnitude of the owner's velocity.

Answer 1

u= 1.17 m/s

θ = 71.21 °

Step-by-step explanation:

Given that

m₁=29.6 kg ,u₁=2.9 j m/s

m₂ = 7.7 kg ,u₂=3.76 i m/s

m= 76.7 kg

The speed of the mass 76.7 kg = u m/s

The linear momentum

m₁ u₁+m₂u₂ = m u

29.6 x 2.9 j + 7.7 x 3.76 i = 76.7 u

76.7 u = 28.95 i +85.84 j

u =0.377 i +1.11 j

The magnitude of the velocity u

`u=√(0.377^2+1.11^2)\ m/s`

u= 1.17 m/s

The direction θ ( angle from eastward direction)

`tan \theta= (1.11)/(0.377)`

θ = 71.21 °

Answer 2

given,

mass of the dog = 29.6 Kg

speed in northward = 2.90 m/s

mass of cat = 7.70 Kg

speed of the cat in eastward = 3.76 m/s

Mass of owner = 76.7 Kg

Momentum of dog

P_y = m₁ x u₁

P_y = 29.6 x 2.9

P_y = 85.84 Kg.m/s

P_x = m₂ x u₂

P_x = 7.7 x 3.76

P_x =28.952 Kg.m/s

magnitude of momentum

`P = √(P_x^2+P_y^2)`

`P = √(28.952^2+85.84^2)`

P = 90.59 Kg.m/s

`\theta = tan^(-1)((P_y)/(P_x))`

`\theta =tan^(-1)((85.84)/(28.952))`

`\theta =71.36^0`