An object is thrown upward with an initial speed of 18.5 m/s from a location 12.2 m above the ground. after reaching its maximum height it falls to the ground. what will its speed be in the last instant prior to its striking the ground?

The speed of the object in the last instant prior to hitting the ground is -24.1 m/s

Explanation:

The equation for the position and velocity of the object will be:

y = y0 + v0 · t + 1/2 · g · t²

v = v0 + g · t

Where:

y = height of the object at time t

v0 = initial velocity

y0 = initial height

g = acceleration due to gravity

t = time

v = velocity at time t

We know that at its maximum height, the velocity of the object is 0. We can obtain the time it takes the object to reach the maximum height and with that time we can calculate the maximum height:

v = v0 + g · t

0 = 18.5 m/s - 9.8 m/s² · t

-18.5 m/s / -9.8 m/s² = t

t = 1.89 s

Now,let´s find the max-height:

y = y0 + v0 · t + 1/2 · g · t²

y = 12.2 m + 18.5 m/s · 1.89 s + 1/2 ·(-9.8 m/s²) · (1.89 s)²

y = 29.7 m

Now, let´s see how much it takes the object to hit the ground:

In that instant, y = 0.

y = y0 + v0 · t + 1/2 · g · t²

0 = 29.7 m + 0 m/s · t - 1/2 · 9.8 m/s² · t²   (notice that v0 = 0 because the object starts from its maximum height, where v = 0)

-29.7 m = -4.9 m/s² · t²

t² = -29.7 m / -4.9 m/s²

t = 2.46 s

Now, we can calculate the speed at t= 2.46 s, the instant prior to hitting the ground.

v = v0 + g · t

v = g · t

v = -9.8 m/s² · 2.46 s

v = -24.1 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

a skateboard rolling across the street - apex