Conservation of energy 1. An object with a mass of 2 kg is moving along a horizo

Question

Conservation of energy

1. 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? (2 points)

2. What is meant by the statement “Energy is conserved”? (2 points)

3. Tarzan swings on a 30.0-m-long vine initially inclined at an angle of 370 with the vertical. What is his speed at the bottom of the swings if he starts from rest? (3 points)

4. Show that the slope of the graph: ((v^2/2) vs h) is negative gravitational acceleration. Use the Law of Conservation of Energy to derive it. (3 points)

i got parts 1-3 already, but i wanted to verify my answers (my answer for part 3 of 2.988m/s seemed kinda sketch)

I dont know at all how to do the last part. any help would be appreciated. thank you

Explanation / Answer

at top there is potential energy and at bottom this energy has converted to kinetic energy

use conservation of energy
potential energy at top = kinetic energy at bottom
m*g*h = 1/2 *m*v^2
g*h = 1/2 *v^2
so,
((v^2/2) / h) = g

to decise sign we can see that when h decreases then v^2 increases
so there is negative correlation between v^2 and h

so slope will be negative

so slope = - g

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