Вертикално движење – проблеми и решенија
1. Ball A threw vertically upward with the забрза of 10 m/s. 1 second later, from the same position, Ball B is thrown vertically upward at the same path, with the speed of 25 m/s. What is the height of ball B when it encounters ball A.
Решение:
In solving the problem of вертикално движење, the vector quantity which direction upward is given a positive sign, the вектор quantity that direction downward is given a negative sign.
Познато:
Почетна брзина (vo) of ball A = 10 m/s
Time interval (t) of ball A = x
Почетна брзина (vo) of ball B = 25 m/s
Time interval (t) of ball B = x – 1
Забрзување поради гравитацијата (g) = -10 m/s2 (given minus sign because the direction of гравитацијата is downward)
Барани: The height of ball B when it encounters ball A (h)
hA = чB
vo t + ½ gt2 = vo t + ½ gt2
10x + ½ (-10) x2 = 25 (x-1) + ½ (-10) (x-1)2
10x - 5x2 = 25 (x-1) – 5 (x-1)2
10x - 5x2 = 25x – 25 – 5 (x2-2x+1)
10x - 5x2 = 25x – 25 – 5x2 +10x -5
10x - 5x2 – 25x + 25 + 5x2 – 10x + 5 = 0
- 5x2 + 5х2 + 10x – 25x – 10x + 25 + 5 = 0
10x – 25x – 10x + 25 + 5 = 0
– 25x + 25 + 5 = 0
– 25x + 30 = 0
– 25x = – 30
x = -30/-25
x = 1.2 секунди
Time interval ball A in air before it encounters ball B = 1.2 seconds
Time interval ball B in air before it encounters ball A = 1.2 seconds – 1 seconds = 0.2 seconds.
The height of ball A when it encounters ball B :
h = vo t + ½ gt2 = (10)(1.2) + 1/2 (-10)(1.2)2 = 12 – 5(1.44) = 12 – 7.2 = 4.8 метарs
The height of ball B when it encounters ball A :
h = vo t + ½ gt2 = (25)(0.2) + 1/2 (-10)(0.2)2 = 5 – 5(0.04) = 5 – 0.2 = 4.8 метарs
1. Прашање: What is meant by vertical motion?
Одговор: Vertical motion refers to the movement of an object upward or downward, typically under the influence of gravitational force.
2. Прашање: How is acceleration due to gravity (g) significant in vertical motion?
Одговор: All objects near Earth’s surface experience a constant acceleration, �, which is approximately 9.81 m/s² downward.
3. Прашање: Can an object have an initial velocity in vertical motion?
Одговор: Yes, objects can have an initial upward or downward velocity when their vertical motion starts.
4. Прашање: What happens to the velocity of a freely falling object?
Одговор: The velocity of a freely falling object increases by approximately 9.81 m/s every second due to Earth’s gravity.
5. Прашање: How is the time of ascent related to the time of descent for a vertically thrown object?
Одговор: For an object thrown upward and then allowed to fall back, the time of ascent equals the time of descent.
6. Прашање: What is the velocity of an object at its maximum height?
Одговор: At maximum height, an object’s vertical velocity becomes zero before it starts descending.
8. Прашање: How does air resistance affect vertical motion?
Одговор: Air resistance opposes motion, reducing acceleration and terminal velocity for falling objects.
9. Прашање: What is terminal velocity?
Одговор: Terminal velocity is the constant maximum velocity reached by a falling object when air resistance equals the force of gravity.
10. Прашање: Can an object have negative acceleration during upward motion?
Одговор: Yes, when an object moves upward against gravity, it has a negative acceleration equal to -g.
12. Прашање: Why is the acceleration negative for objects thrown upward?
Одговор: Because acceleration due to gravity acts downward, it’s considered negative for objects moving in the opposite direction.
14. Прашање: What is free fall?
Одговор: Free fall is the motion of an object under the sole influence of gravity, with no other forces acting on it.
15. Прашање: How does the motion of an object differ when thrown downward versus when dropped?
Одговор: Both experience acceleration due to gravity. However, an object thrown downward has an additional initial velocity, making it reach the ground faster than one simply dropped.
16. Прашање: What factors affect an object’s terminal velocity?
Одговор: Factors include object’s mass, shape, surface area, and the medium’s density and viscosity it’s falling through.
17. Прашање: Does an object in vertical motion possess kinetic and potential energy?
Одговор: Yes, an object’s kinetic energy increases as it falls, while its potential energy decreases, and vice-versa during ascent.
18. Прашање: Why does an object’s velocity change during vertical motion?
Одговор: The gravitational force causes a constant acceleration, changing the object’s velocity until it reaches terminal velocity or changes direction.
19. Прашање: Can vertical motion be described as uniformly accelerated motion?
Одговор: Yes, in the absence of air resistance, vertical motion under gravity is uniformly accelerated with an acceleration of .
20. Прашање: How is the conservation of energy principle applied to vertical motion?
Одговор: The sum of kinetic and potential energy remains constant during vertical motion, assuming no energy loss to air resistance.
Understanding vertical motion is essential in classical mechanics and has practical applications ranging from sports science to engineering and safety regulations.
