4. Peter Pan. You have been hired for a production of Peter Pan. In Act 2, Peter Pan
is supposed to "fly down" and meet her followers. The actress of mass m₁ playing the part
must descend a vertical distance of 5.00 m in 2.70 seconds at constant acceleration. This is to
be accomplished by connecting a counterweight of mass m₂ to her by a wire. As the weights
moves up on a frictionless plane inclined at an angle 0, she moves down at the same constant acceleration. The wire passes over a frictionless, massless pulley.
As the physics expert, you are asked to figure out the required mass of the counterweight and
the tension in the wire connecting the actress to the counterweight.

a) Show that the constant acceleration to let the actress move through a distance of 5.00 m in 2.70 seconds is a = 1.37 m/s².
b) Plug the values of m₁ = 45.0 kg, g, a, and 0 = 50.0° into your expression for m₂ to find the mass of the counterweight.
c) Obtain the value for Tension in the wire using the values of m₁, g and a.
d) Find the value of the counterweight mass that would allow the 45.0-kg actress to hang motionless or "float" above her followers if the angle of the plane is 0 = 50.0°