Introduction:
In this scenario, we have a ball of mass "m" which is thrown at an angle theta with the horizontal and has an initial velocity u. We need to determine the magnitude of change in momentum during its flight in a time interval of "t".

Understanding the problem:
To solve this problem, we need to understand the concept of momentum and how it changes during the flight of the ball. Momentum is defined as the product of an object's mass and its velocity. It is a vector quantity and its magnitude can change if the object experiences an external force.

Analysis:
During the flight of the ball, the only external force acting on it is the force due to gravity. This force acts vertically downwards and does not change the horizontal component of momentum. Therefore, we only need to consider the change in the vertical component of momentum.

Calculating the change in vertical component of momentum:
The initial vertical component of momentum is given by mv sin(theta), where v is the magnitude of the initial velocity u. The final vertical component of momentum is zero since the ball reaches its maximum height and then falls back down. Therefore, the change in vertical component of momentum is -mv sin(theta).

Calculating the time of flight:
To calculate the time of flight, we can use the equation of motion: h = ut sin(theta) - (1/2)gt^2, where h is the maximum height reached by the ball. Rearranging this equation, we get -gt^2 + ut sin(theta) - h = 0. This is a quadratic equation in terms of t. Solving this equation, we can find the time of flight.

Calculating the magnitude of change in momentum:
The magnitude of change in momentum is given by the absolute value of the change in vertical component of momentum divided by the time of flight. Therefore, it is equal to |-mv sin(theta)| / t = mgt sin(theta) / t.

Final answer:
The magnitude of change in momentum during the flight of the ball in a time interval of "t" is mgt sin(theta). Therefore, the correct option is (3) mgt sin(theta).

C is correct