A5.0-kg rabbit and a 12-kg irish setter have the same kinetic energy. if the setter is running at speed 4.9 m/s, how fast is the rabbit running?

7.59 m/s

Explanation:

Kinetic Energy: This is defined as the energy possessed by a body due to its motion. The S.I unit of kinetic energy is Joules (J).

Mathematically, kinetic energy is represented as,

Ek = 1/2mv² Equation 1

Where Ek = Kinetic Energy, m = mass, v = velocity.

From the question,

Kinetic energy of the rabbit = Kinetic energy of the setter

1/2m₁v₁² = 1/2m₂v₂² equation 2

Where m₁ = mass of the rabbit, v₁ = velocity of the rabbit, m₂ = mass of the setter, v₂ = velocity of the setter.

making v₁ the subject of the equation

v₁ = v₂√(m₂/m₁) Equation 3

Given: m₁ = 5.0 kg, m₂ = 12.0 kg, v₂ = 4.9 m/s.

Substituting into equation 3

v₁ = 4.9√(12/5)

v₁  = 4.9√2.4

v₁ = 4.9×1.549

v₁ = 7.59 m/s

Thus the rabbit is 7.59 m/s fast

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west