Calculate the magnitude of the initial velocity vector of the object. (Express your answer to two significant figures.)

Question

An object experiences a constant acceleration of 2.00 m/s² along the -x axis for 2.70 s, attaining a velocity of 18.0 m/s in a direction 47 from the +x axis.

Answer 1

Express the initial velocity in term of i and j vector components.

V = V cosθ î + Vsinθ j

The change in the velocity is ΔV = a_x.t = (- 2m/s² î)(2.70s) = - 5.40 î m/s

The final velocity is V_f = (V cosθ - 5.40) î + Vsinθ j

The final velocity is given as 18 m/s at 47^o to the + x axis = 18 cos47^o î + 18 sin47^o j.

Hence, (V cosθ - 5.40) î + Vsinθ j = 18 cos47^o î + 18 sin47^o j

This last equation provides the following component equations.

V cosθ - 5.40 = 18 cos47^o

Vsinθ = 18 sin47^o

You now have two equations with 2 unknowns, V and θ, which you should be able to solve.

If you need additional assistance to solve this problem or any other problem, you can schedule an appointment.