A20 kg child is on a swing that hangs from 3.0-m-long chains. what is her maximum speed if she swings out to a 49 ∘ angle?

L = length of the chain = 3 m

θ = angle with the vertical = 49 deg

h = height gained

In triangle ABD

Cosθ = AB/AD

Cosθ = AB/L

AB = L Cosθ

BC = AC - AB = L - L Cosθ

so h =  L - L Cosθ

inserting the values

h =  (3) - (3) Cos49 = 1.032 m

v = maximum speed at the bottom of the swing

Using conservation of energy

kinetic energy at the bottom of the swing = potential energy at the maximum height

(0.5) m v² = mg h

v = sqrt(2gh)

v = sqrt(2 x 9.8 x 1.032)

v = 4.5 m/s

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.