Two teenagers are pulling on ropes attached to a tree. The angle between the ropes is 30.0°30.0° . David pulls with a force of 400.0 N and Stephanie pulls with a force of 300.0 N. (a) Find the component form of the net force. (b) Find the magnitude of the resultant (net) force on the tree and the angle it makes with David’s rope.

The magnitude of the resultant force , is 676.643 N

The angle it makes with David;s rope is 77.19°

Explanation:

Here we have

David's force F₁ = 400 N and direction of F₁ = horizontal θ₁ = 0

Stephanie's force F₂ = 300.0 N direction of F₂ = θ₂ = 30°

The angle between the ropes θ = 30°

Therefore we resolve the forces applied by the two teenagers as follows

F₁ₓ = F₁×cos (0) = F₁ = 400.0 N

=  F₁×sin (0) = 0 N

Also

F₂ₓ = F₂×cos (θ₂) = 300 ×cos (30)= 259.81 N

=  F₂×sin (θ₂) =  300 ×sin (30)= 150 N

Therefore, the combined force of both teenagers is;

∑Fₓ = F₁ₓ + F₂ₓ = 400.0 N + 259.81 N = 659.81 N and

∑ = + = 0 N + 150 N =150 N

The resultant force is given by

=  

The magnitude of the resultant force is, ;

The angle it makes with David's rope is

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.