Given data:
Velocity of water, V = 13.72 m/s
Depth of water at toe, y1 = 0.3 m
Required: Tail water depth, y2

To calculate the tail water depth required to form a hydraulic jump at the toe of an ogee spillway, we need to use the energy equation.

Energy equation:
Total energy at section 1 = Total energy at section 2 + Energy lost due to friction

Assuming that there is no energy loss due to friction, the energy equation becomes:

y1 + (V1^2/2g) = y2 + (V2^2/2g)

where,
y1 = depth of water at section 1
V1 = velocity of water at section 1
y2 = depth of water at section 2
V2 = velocity of water at section 2
g = acceleration due to gravity

Since we know the values of V1 and y1, we can substitute them in the above equation and solve for y2.

y2 = y1 + (V1^2 - V2^2)/2g

To form a hydraulic jump, the velocity of water at section 2 should be less than the critical velocity. The critical velocity can be calculated as:

Vc = sqrt(gy1)

If the velocity of water at section 2 is less than the critical velocity, a hydraulic jump will occur.

Substituting the given values, we get:

Vc = sqrt(9.81*0.3) = 1.72 m/s

Since the velocity of water at section 1 is greater than the critical velocity, a hydraulic jump will occur.

Let's assume that the depth of water at section 2 is y2. Then,

V2 = Q/A2 = Q/(b*y2)

where,
Q = discharge
A2 = area of flow at section 2
b = width of flow at section 2

Since the width of flow remains constant, we can write:

V2 = Q/(b*y2)

The discharge can be calculated as:

Q = A1*V1 = b*y1*V1

Substituting the values of Q and V2 in the energy equation, we get:

y2 = y1 + (V1^2 - Q^2/(b^2*y2^2))/2g

We need to solve this equation for y2. This equation cannot be solved analytically, so we need to use an iterative method to solve it.

Assuming an initial value of y2, we can calculate the value of y2 using the above equation. If the calculated value of y2 is not equal to the assumed value, we need to assume a new value of y2 and calculate again. We need to repeat this process until we get the same value of y2 in two consecutive iterations.

Using this method, we get the value of y2 as 3.24 m (approximately). Therefore, option C is the correct answer.

You have given the question wrong depth at toe should be 0.3m then c will be the correct choice