Physics, 30.05.2021 04:20 vale2652

An object whose weight is 100 lbf experiences a decrease in kinetic energy of 500 ft-lbf and an increase in potential energy of 1500 ft-lbf. The initial velocity and elevation of the object, each relative to the surface of the earth, are 40 ft/s and 30 ft, respectively. Required:
a. Find final velocity in ft/s.
b. Find final elevation.

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Answer from: LuckyCharms988

a) the final velocity is 35.75 ft/s

b) The final elevation is 45 ft

Explanation:

Given the data in the question;

Weight of object; W = 100 lbf

Change in kinetic energy; ΔE = 500 ft-lb

$\frac{1}{2}$ m v_i^2 - $\frac{1}{2}$ m v_f^2 = ΔE

$\frac{1}{2}$ m v_i^2 - $\frac{1}{2}$ m v_f^2 = 500

multiply both sides by 2

m v_i^2 - m v_f^2 = 1000

m( v_i^2 - v_f^2 ) = 1000

v_i^2 - v_f^2 = 1000/m

v_i^2 - v_f^2 = (1000)(g) / W

we know that, acceleration due to gravity g = 9.8 m/s² = 32.18 ft/s²

so we substitute

v_i^2 - v_f^2 = (1000)(32.18) / 100

v_i^2 - v_f^2 = 32180 / 100

v_i^2 - v_f^2 = 321.8

since The initial velocity v_i is given to be 40 ft/s;

(40)² - v_f^2 = 321.8

1600 - v_f^2 = 321.8

v_f^2 = 1600 - 321.8

v_f^2 = 1278.2

v_f = √1278.2

v_f = 35.75 ft/s

Therefore, the final velocity is 35.75 ft/s

we know that;

change in potential energy is;

ΔP.E = mg( h - h )

given that; increase in potential energy; ΔP.E = 1500 ft-lbf

and mg = Weight = 100 lbf

we substitute

1500 = 100( h - h )

h - h = 1500 / 100

h - h = 15 ft

given that, elevation of the object; h = 30 ft

h - 30 ft = 15 ft

h = 15 ft + 30 ft

h = 45 ft

Therefore, The final elevation is 45 ft

Answer from: Quest

Is a vector quantity that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

Answer from: Quest

It equals just about 6,300 km per hour each day an week

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An object whose weight is 100 lbf experiences a decrease in kinetic energy of 500 ft-lbf and an incr...

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