Neʻe kū pololei - nā pilikia a me nā hoʻonā
1. Hoʻolei pololei ʻo Pōpō A i luna me ka ka mämä holo o 10 m/s. 1 kekona ma hope mai, mai ke kūlana like, ua hoʻolei ʻia ka Pōpō B i luna ma ke ala like, me ka wikiwiki o 25 m/s. He aha ke kiʻekiʻe o ka pōpō B i ka wā e hālāwai ai me ka pōpō A.
Lōlā:
I ka hoʻoponopono ʻana i ka pilikia o neʻe kū pololei, ka nui vector nona ke kuhikuhi i luna i hāʻawi ʻia i kahi hōʻailona maikaʻi, ka veme ua hāʻawi ʻia ka nui i ke kuhikuhi i lalo i kahi hōʻailona maikaʻi ʻole.
ʻIke ʻia:
Ka wikiwiki mua (vo) of ball A = 10 m/s
Time interval (t) of ball A = x
Ka wikiwiki mua (vo) of ball B = 25 m/s
Time interval (t) of ball B = x – 1
ʻO ka wikiwiki ma muli o ka umekaumaha (g) = -10 m/s2 (given minus sign because the direction of umekaumaha is downward)
Makemake ʻia: The height of ball B when it encounters ball A (h)
hA = hB
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 +5x2 + 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 mikas
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 mikas
1. Nīnau: What is meant by vertical motion?
pane mai: Vertical motion refers to the movement of an object upward or downward, typically under the influence of gravitational force.
2. Nīnau: How is acceleration due to gravity (g) significant in vertical motion?
pane mai: All objects near Earth’s surface experience a constant acceleration, �, which is approximately 9.81 m/s² downward.
3. Nīnau: Can an object have an initial velocity in vertical motion?
pane mai: Yes, objects can have an initial upward or downward velocity when their vertical motion starts.
4. Nīnau: What happens to the velocity of a freely falling object?
pane mai: The velocity of a freely falling object increases by approximately 9.81 m/s every second due to Earth’s gravity.
5. Nīnau: How is the time of ascent related to the time of descent for a vertically thrown object?
pane mai: For an object thrown upward and then allowed to fall back, the time of ascent equals the time of descent.
6. Nīnau: What is the velocity of an object at its maximum height?
pane mai: At maximum height, an object’s vertical velocity becomes zero before it starts descending.
8. Nīnau: How does air resistance affect vertical motion?
pane mai: Air resistance opposes motion, reducing acceleration and terminal velocity for falling objects.
9. Nīnau: What is terminal velocity?
pane mai: Terminal velocity is the constant maximum velocity reached by a falling object when air resistance equals the force of gravity.
10. Nīnau: Can an object have negative acceleration during upward motion?
pane mai: Yes, when an object moves upward against gravity, it has a negative acceleration equal to -g.
12. Nīnau: Why is the acceleration negative for objects thrown upward?
pane mai: Because acceleration due to gravity acts downward, it’s considered negative for objects moving in the opposite direction.
14. Nīnau: What is free fall?
pane mai: Free fall is the motion of an object under the sole influence of gravity, with no other forces acting on it.
15. Nīnau: How does the motion of an object differ when thrown downward versus when dropped?
pane mai: 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. Nīnau: What factors affect an object’s terminal velocity?
pane mai: Factors include object’s mass, shape, surface area, and the medium’s density and viscosity it’s falling through.
17. Nīnau: Does an object in vertical motion possess kinetic and potential energy?
pane mai: Yes, an object’s kinetic energy increases as it falls, while its potential energy decreases, and vice-versa during ascent.
18. Nīnau: Why does an object’s velocity change during vertical motion?
pane mai: The gravitational force causes a constant acceleration, changing the object’s velocity until it reaches terminal velocity or changes direction.
19. Nīnau: Can vertical motion be described as uniformly accelerated motion?
pane mai: Yes, in the absence of air resistance, vertical motion under gravity is uniformly accelerated with an acceleration of .
20. Nīnau: How is the conservation of energy principle applied to vertical motion?
pane mai: 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.
