Question

Susan is running to the right, in the +x-direction, at 2 m/s. A bird flies past her, traveling to the left at 10 m/s. What is the bird's velocity in Susan's reference frame?

Answer 1

The concept of relative velocity can be found the speed of the bird respecting susan v = -12 m / s. The negative sign indicates that the bird is approaching susan

given parameter

• the speeds of Susam and the bird

to find

• the relative speed between Susan and the bird

Velocity is a vector unit, therefore, in addition to magnitude, it has direction and sense, therefore, to make the sum of the same quantities, vector relations must be used

         v₁ = v₂ + v₃

where v₁, v₂ and v₃ are velocity and the bold letters indicate vectors

in this case Susan and the bird go on the x axis therefore the algebra is reduced to the algebraic sum. We will assume that the positive direction is to the right of the x-axis, consequently the velocities are:

Susan       v_{st} = 2 m / s

Bird          v_{bt} = - 10 m / s

The relative velocity is the vector sum of the velocities of the bodies, one way to perform this sum is by using subscripts

           v_{pt} =   v_{ps} + v_{st}

           

Where  v_{ps} is the speed of the bird relative to susan, v_{st} is the speed of susan relative to the ground, and v_{pt} is the speed of the bird relative to the ground.

            v_{ps} = v_{pt} - v_{st}

            v_{ps} = -10 - 2

            v_{ps} = - 12 m / s

Using the concept of relative velocity, the velocity of the bird respecting susan v = -12 m/s can be found. The negative sign indicates that the bird is approaching susab.

Learn more about relative velocity here:

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