Вертикальний рух – проблеми та рішення
1. Ball A threw vertically upward with the швидкість 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.
Рішення:
In solving the problem of вертикальний рух, the vector quantity which direction upward is given a positive sign, the вектор quantity that direction downward is given a negative sign.
Відомо:
Початкова швидкість (vo) of ball A = 10 m/s
Time interval (t) of ball A = x
Початкова швидкість (vo) of ball B = 25 m/s
Time interval (t) of ball B = x – 1
Прискорення за рахунок сили тяжіння (g) = -10 m/s2 (given minus sign because the direction of вага is downward)
Розшукується: The height of ball B when it encounters ball A (h)
hA = годB
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 +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 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 метрs
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 метрs
1. Питання: What is meant by vertical motion?
Відповідь: Vertical motion refers to the movement of an object upward or downward, typically under the influence of gravitational force.
2. Питання: How is acceleration due to gravity (g) significant in vertical motion?
Відповідь: All objects near Earth’s surface experience a constant acceleration, , which is approximately 9.81 m/s² downward.
3. Питання: Can an object have an initial velocity in vertical motion?
Відповідь: Yes, objects can have an initial upward or downward velocity when their vertical motion starts.
4. Питання: What happens to the velocity of a freely falling object?
Відповідь: The velocity of a freely falling object increases by approximately 9.81 m/s every second due to Earth’s gravity.
5. Питання: How is the time of ascent related to the time of descent for a vertically thrown object?
Відповідь: For an object thrown upward and then allowed to fall back, the time of ascent equals the time of descent.
6. Питання: What is the velocity of an object at its maximum height?
Відповідь: At maximum height, an object’s vertical velocity becomes zero before it starts descending.
8. Питання: How does air resistance affect vertical motion?
Відповідь: Air resistance opposes motion, reducing acceleration and terminal velocity for falling objects.
9. Питання: What is terminal velocity?
Відповідь: Terminal velocity is the constant maximum velocity reached by a falling object when air resistance equals the force of gravity.
10. Питання: Can an object have negative acceleration during upward motion?
Відповідь: Yes, when an object moves upward against gravity, it has a negative acceleration equal to -g.
12. Питання: Why is the acceleration negative for objects thrown upward?
Відповідь: Because acceleration due to gravity acts downward, it’s considered negative for objects moving in the opposite direction.
14. Питання: What is free fall?
Відповідь: Free fall is the motion of an object under the sole influence of gravity, with no other forces acting on it.
15. Питання: How does the motion of an object differ when thrown downward versus when dropped?
Відповідь: 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. Питання: What factors affect an object’s terminal velocity?
Відповідь: Factors include object’s mass, shape, surface area, and the medium’s density and viscosity it’s falling through.
17. Питання: Does an object in vertical motion possess kinetic and potential energy?
Відповідь: Yes, an object’s kinetic energy increases as it falls, while its potential energy decreases, and vice-versa during ascent.
18. Питання: Why does an object’s velocity change during vertical motion?
Відповідь: The gravitational force causes a constant acceleration, changing the object’s velocity until it reaches terminal velocity or changes direction.
19. Питання: Can vertical motion be described as uniformly accelerated motion?
Відповідь: Yes, in the absence of air resistance, vertical motion under gravity is uniformly accelerated with an acceleration of .
20. Питання: How is the conservation of energy principle applied to vertical motion?
Відповідь: 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.
