Question

A small submarine is underwater and moving horizontally at the same constant speed as the northward current in a straight, level section of a river. It releases a sensor that will float in the water. If resistance is negligible, what is the shape of the path followed by the sensor?

Answer 1

The sensor released by a submarine moving in a current at constant speed will follow a straight path if resistance is negligible.

Step-by-step explanation:

If a submarine is moving underwater at the same constant speed as the northward current and releases a sensor that will float in the water, and assuming resistance is negligible, the shape of the path followed by the sensor will be a straight line. This is because the sensor will continue to move at the same speed and direction as the current and the submarine due to its inertia. It gets an initial velocity from the submarine, which is identical to the velocity of the water current, thus the sensor will co-move with the water. If there are no external forces acting on the sensor, like resistance, to change its path, it will follow a straight trajectory.

Answer 2

Parabolic

Step-by-step explanation:

Since resistance is negligible, there are no forces in the x direction, so according to Newton's second law, the x component of the acceleration is 0.

∑F = ma

aₓ = 0

In the y direction, there are two forces: buoyancy upwards and weight downwards. Both are constant, so the acceleration is constant:

∑F = ma

B − W = maᵧ

aᵧ = (B − W) / m

Using kinematics, the horizontal and vertical displacements are:

x = v₀ₓ t

y = ½ aᵧ t²

Therefore, the path taken by the sensor is a parabola y = kx², where k = aᵧ / (2 v₀ₓ²) = (B − W) / (2m v₀ₓ²).