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).

given data:

determine the horse power (h.p) = ?

force applied to move the box(f) = 10 pounds,

box lifted from a distance         (d) = 3 feet

time taken to lift                         (t) = 10 sec,

the horse power is defined as amount of work required to move a load. the horse power is equal to 550 foot-pound per second

                  1 h.p   = 550 foot-pound/second

it can also be defined as the the load that need to be move a body for certain distance in a certain amount of time.

mathematically,

                      h.p = (force × distance)/ time

                            = (10 × 3)/ 10

                            = 30/10

                            = 3 foot -pound/sec

hence, the horse power is needed to move the box is 3 foot-pound/second

important note: 1 h.p = 550 foot-pound/second = 746 watts

if the thermos has a vacuum innner, then heat through conv currents and conduction are reduced = vacuum flask