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?

Parabolic

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).

do you have a formula possibly