a body is thrown vertically upward from the earth's surface and it took 8 seconds to return to its original position . find out the initial velocity with which it was thrown up

The initial velocity with which the body was thrown up is 39.2 m/s

Explanation:

The given parameters for the body are;

The time it takes the body to return back to its initial position = 8 seconds

To answer the question, we make use of the kinematic equation of motion, v = u - g·t

Where

v = The final velocity of the body = 0 m/s at the maximum height

u = The initial velocity

g = The acceleration due to gravity = 9.8 m/s²

t = The time in which the body spends in the air

Therefore, at maximum height, we have;

v = 0 = u - g·t

u = g·t

t = u/g

From h = 1/2gt², which gives t = √(2·h/g), the time the body takes to maximum height = The time the body takes to return to its original position from maximum height.

Therefore, the total time in which the body is in the air = 2 × t = 2× u/g

∴

The total time in which the body is in the air = The time it takes the body to return back to its initial position after being thrown = 2 × t =  8 seconds

∴ 2 × t = 8 s = 2 × u/g

8 s = 2 × u/g

u = (8 s × g)/2

∴ u = (8 s × 9.8 m/s²)/2 = 39.2 m/s

The initial velocity with which the body was thrown up = u = 39.2 m/s.

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

the answer is a. the yacht traveled from the dock north to the 200-meter marker in the bay in less than 5 minutes, giving the passengers several more hours to fish.

im doing peak rn so sry if its wrong