Тік қозғалыс – мәселелер және оларды шешу жолдары
1. А добы тігінен жоғары лақтырылады жылдамдық 10 м/с жылдамдықпен. 1 секундтан кейін, сол қалыптан В добы сол траектория бойынша 25 м/с жылдамдықпен тігінен жоғары лақтырылды. В добы А добымен соқтығысқан кезде қандай биіктікке ие болады?
Шешімі:
Мәселені шешуде тік қозғалыс, жоғары қарай бағыты оң таңбамен берілген векторлық шама, векторы төмен қарай бағытталған шамаға теріс таңба беріледі.
Белгілі:
Бастапқы жылдамдық (vo) of ball A = 10 m/s
Time interval (t) of ball A = x
Бастапқы жылдамдық (vo) of ball B = 25 m/s
Time interval (t) of ball B = x – 1
Ауырлық күшінің әсерінен үдеу (g) = -10 м/с2 (given minus sign because the direction of ауырлық is downward)
Қажетті: The height of ball B when it encounters ball A (h)
hA = сағB
vo t + ½ gt2 = vo t + ½ gt2
10x + ½ (-10) x2 = 25 (x-1) + ½ (-10) (x-1)2
10х - 5х2 = 25 (x-1) – 5 (x-1)2
10х - 5х2 = 25x – 25 – 5 (x2-2x+1)
10х - 5х2 = 25x – 25 – 5x2 +10x –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 t + ½ gt2 = (10)(1.2) + 1/2 (-10)(1.2)2 = 12 – 5(1.44) = 12 – 7.2 = 4.8 метрs
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 метрs
1. Сұрақ: What is meant by vertical motion?
Жауап: Vertical motion refers to the movement of an object upward or downward, typically under the influence of gravitational force.
2. Сұрақ: How is acceleration due to gravity (g) significant in vertical motion?
Жауап: All objects near Earth’s surface experience a constant acceleration, , which is approximately 9.81 m/s² downward.
3. Сұрақ: Can an object have an initial velocity in vertical motion?
Жауап: Yes, objects can have an initial upward or downward velocity when their vertical motion starts.
4. Сұрақ: What happens to the velocity of a freely falling object?
Жауап: The velocity of a freely falling object increases by approximately 9.81 m/s every second due to Earth’s gravity.
5. Сұрақ: How is the time of ascent related to the time of descent for a vertically thrown object?
Жауап: For an object thrown upward and then allowed to fall back, the time of ascent equals the time of descent.
6. Сұрақ: What is the velocity of an object at its maximum height?
Жауап: At maximum height, an object’s vertical velocity becomes zero before it starts descending.
8. Сұрақ: How does air resistance affect vertical motion?
Жауап: Air resistance opposes motion, reducing acceleration and terminal velocity for falling objects.
9. Сұрақ: What is terminal velocity?
Жауап: Terminal velocity is the constant maximum velocity reached by a falling object when air resistance equals the force of gravity.
10. Сұрақ: Can an object have negative acceleration during upward motion?
Жауап: Yes, when an object moves upward against gravity, it has a negative acceleration equal to -g.
12. Сұрақ: Why is the acceleration negative for objects thrown upward?
Жауап: Because acceleration due to gravity acts downward, it’s considered negative for objects moving in the opposite direction.
14. Сұрақ: What is free fall?
Жауап: Free fall is the motion of an object under the sole influence of gravity, with no other forces acting on it.
15. Сұрақ: How does the motion of an object differ when thrown downward versus when dropped?
Жауап: 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. Сұрақ: What factors affect an object’s terminal velocity?
Жауап: Factors include object’s mass, shape, surface area, and the medium’s density and viscosity it’s falling through.
17. Сұрақ: Does an object in vertical motion possess kinetic and potential energy?
Жауап: Yes, an object’s kinetic energy increases as it falls, while its potential energy decreases, and vice-versa during ascent.
18. Сұрақ: Why does an object’s velocity change during vertical motion?
Жауап: The gravitational force causes a constant acceleration, changing the object’s velocity until it reaches terminal velocity or changes direction.
19. Сұрақ: Can vertical motion be described as uniformly accelerated motion?
Жауап: Yes, in the absence of air resistance, vertical motion under gravity is uniformly accelerated with an acceleration of .
20. Сұрақ: How is the conservation of energy principle applied to vertical motion?
Жауап: 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.
