Босоо хөдөлгөөн - асуудал ба шийдэл
1. Ball A threw vertically upward with the хурд 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.
Шийдэл:
In solving the problem of босоо хөдөлгөөн, the vector quantity which direction upward is given a positive sign, the вектор quantity that direction downward is given a negative sign.
Мэдэгдэж байгаа:
Анхны хурд (vo) of ball A = 10 m/s
Time interval (t) of ball A = x
Анхны хурд (vo) of ball B = 25 m/s
Time interval (t) of ball B = x – 1
Хүндийн хүчний нөлөөгөөр хурдатгал (g) = -10 м/с2 (given minus sign because the direction of хүндийн хүчний is downward)
Хүссэн: The height of ball B when it encounters ball A (h)
hA =цB
vo т + ½ гт2 = vo т + ½ гт2
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 + 10х – 5
10x - 5x2 – 25x + 25 + 5x2 – 10x + 5 = 0
- 5х2 + 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 seconds
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 т + ½ гт2 = (10)(1.2) + 1/2 (-10)(1.2)2 = 12 – 5(1.44) = 12 – 7.2 = 4.8 метрийнs
The height of ball B when it encounters ball A :
h = vo т + ½ гт2 = (25)(0.2) + 1/2 (-10)(0.2)2 = 5 – 5(0.04) = 5 – 0.2 = 4.8 метрийнs
1. Асуулт: What is meant by vertical motion?
Хариулт: Vertical motion refers to the movement of an object upward or downward, typically under the influence of gravitational force.
2. Асуулт: How is acceleration due to gravity (g) significant in vertical motion?
Хариулт: All objects near Earth’s surface experience a constant acceleration, , which is approximately 9.81 m/s² downward.
3. Асуулт: Can an object have an initial velocity in vertical motion?
Хариулт: Yes, objects can have an initial upward or downward velocity when their vertical motion starts.
4. Асуулт: What happens to the velocity of a freely falling object?
Хариулт: The velocity of a freely falling object increases by approximately 9.81 m/s every second due to Earth’s gravity.
5. Асуулт: How is the time of ascent related to the time of descent for a vertically thrown object?
Хариулт: For an object thrown upward and then allowed to fall back, the time of ascent equals the time of descent.
6. Асуулт: What is the velocity of an object at its maximum height?
Хариулт: At maximum height, an object’s vertical velocity becomes zero before it starts descending.
8. Асуулт: How does air resistance affect vertical motion?
Хариулт: Air resistance opposes motion, reducing acceleration and terminal velocity for falling objects.
9. Асуулт: What is terminal velocity?
Хариулт: Terminal velocity is the constant maximum velocity reached by a falling object when air resistance equals the force of gravity.
10. Асуулт: Can an object have negative acceleration during upward motion?
Хариулт: Yes, when an object moves upward against gravity, it has a negative acceleration equal to -g.
12. Асуулт: Why is the acceleration negative for objects thrown upward?
Хариулт: Because acceleration due to gravity acts downward, it’s considered negative for objects moving in the opposite direction.
14. Асуулт: What is free fall?
Хариулт: Free fall is the motion of an object under the sole influence of gravity, with no other forces acting on it.
15. Асуулт: How does the motion of an object differ when thrown downward versus when dropped?
Хариулт: 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. Асуулт: What factors affect an object’s terminal velocity?
Хариулт: Factors include object’s mass, shape, surface area, and the medium’s density and viscosity it’s falling through.
17. Асуулт: Does an object in vertical motion possess kinetic and potential energy?
Хариулт: Yes, an object’s kinetic energy increases as it falls, while its potential energy decreases, and vice-versa during ascent.
18. Асуулт: Why does an object’s velocity change during vertical motion?
Хариулт: The gravitational force causes a constant acceleration, changing the object’s velocity until it reaches terminal velocity or changes direction.
19. Асуулт: Can vertical motion be described as uniformly accelerated motion?
Хариулт: Yes, in the absence of air resistance, vertical motion under gravity is uniformly accelerated with an acceleration of .
20. Асуулт: How is the conservation of energy principle applied to vertical motion?
Хариулт: 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.
