You drop a rock into a deep well and hear the sounds of it hitting the bottom 5.50 s later. if the speed of sound is 340 m/s, determine the depth of the well.

The depth of well equals 120.47 meters.

Explanation:

The time it takes the sound to reach our ears is the sum of:

1) Time taken by the rock to reach the well floor.

2) Time taken by the sound to reach our ears.

The Time taken by the rock to reach the well floor can be calculated using second equation of kinematics as:

where,

'u' is initial velocity

't' is the time to cover a distance 'h' which in our case shall be the depth of well.

'g' is acceleration due to gravity

Since the rock is dropped from rest hence we infer that the initial velocity of the rock =0 m/s.

Thus the time to reach the well base equals

Since the propagation of the sound back to our ears takes place at constant speed hence the time taken in the part 2 is calculated as

Now since it is given that

Upon solving we get

Solving the quadratic equation for 'h' we get

h = 120.47 meters.

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

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach