To solve this problem it is necessary to use the concepts related to Snell's law.
Snell's law establishes that reflection is subject to

Where,
Angle between the normal surface at the point of contact
n = Indices of refraction for corresponding media
The total internal reflection would then be given by





Therefore the
would be equal to



Therefore the largest value of the angle α is 30.27°
The force applied by the man is 60 N
Explanation:
We can solve this problem by applying Newton's second law, which states that:
(1)
where
is the net force acting on the child+cart
m is the mass of the child+cart system
a is their acceleration
In this problem, we have:
m = 30.0 kg is the mass

And there are two forces acting on the child+cart system:
- The forward force of pushing, F
- The force resisting the cart motion, R = 15.0 N
Therefore we can write the net force as

where R is negative since its direction is opposite to the motion
So eq.(1) can be rewritten as

And solving for F,

Learn more about Newton's second law:
brainly.com/question/3820012
#LearnwithBrainly