Help me please with full steps. no steps no rate An object with a mass of 2 kg i

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Help me please with full steps. no steps no rate

An object with a mass of 2 kg is moving along a horizontal surface with velocity components vx=4 m/s and vy= -3.5 m/s. What is the objects speed? What is its kinetic energy? What is meant by the statement "Energy is conserved"? Tarzan swings on a 30.0-m-long vine initially inclined at an angle of 37 degree with the vertical. What is his speed at the bottom of the swings if he starts from rest? Show that the slope of the graph: (v/2 vs h) is negative gravitational acceleration. Use the Law of Conservation of Energy to derive it.

Explanation / Answer

1. speed = sqrt(vx^2 + vy^2) = 5.32 m/s

2. total energy of system will always be same.
so at every point potential energy + kinetic energy = constant
P.Einitial +K.E initial   = P.Efinal + K.Efinal

3. h = 30 ( 1-cos37) = 6.04 m
mv^2 /2 = mgh
v =10.88 m/s

4. from energy conservation ,
K.E + P.E = constant
mv^2 /2 + mgh = c
v^2/2 = -g (h) + c
compare with y = mx + c
slope = m = -g

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