introduction to projectile motion — Transcript

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1. 0:00suppose you and your friend are standing
2. 0:02at the edge of a cliff
3. 0:04your friend drops a stone straight down
4. 0:07and with great speed you throw a similar
5. 0:09stone horizontally
6. 0:11the question is which stone will land on
7. 0:14the water surface last does your
8. 0:16intuition tell you that since you threw
9. 0:18the stone with greater speed the stone
10. 0:20will take more time to land
11. 0:22if so you are wrong
12. 0:24both stones will actually land at the
13. 0:26same time
14. 0:27welcome to the interesting world of
15. 0:29projectile motion
16. 0:31let's go over some fundamental concepts
17. 0:35when you throw a ball at an angle it
18. 0:37never goes straight like this
19. 0:39instead it will have an elegant curved
20. 0:42path more specifically a parabolic path
21. 0:45this kind of projectile motion happens
22. 0:48due to the effect of gravity
23. 0:50when thrown at an angle the object has
24. 0:52two components of velocity one
25. 0:55horizontal and one vertical
26. 0:57the gravitational force always acts
27. 0:59vertically
28. 1:00when a force acts on a moving object
29. 1:03vertically the horizontal component of
30. 1:05velocity never changes
31. 1:07only the vertical component of the
32. 1:09object's velocity will change due to the
33. 1:11vertical force
34. 1:12therefore the initial horizontal
35. 1:14component of velocity you have given
36. 1:17will also not change throughout the
37. 1:18motion of the object
38. 1:20let's analyze this more closely and see
39. 1:22how the variation of the vertical
40. 1:24component of velocity affects the shape
41. 1:27of the trajectory
42. 1:29the horizontal and vertical distance
43. 1:31traveled by the object for a small time
44. 1:33interval is shown here
45. 1:35its complete motion will be as shown
46. 1:39since the horizontal component of
47. 1:40velocity does not change with time with
48. 1:43an equal time interval the ball will
49. 1:45travel the same distance horizontally
50. 1:48however the vertical component of
51. 1:50velocity has been reduced due to the
52. 1:52effect of gravity thus the distance
53. 1:55traveled vertically in this time
54. 1:57interval will be lesser
55. 2:00just continue this logic for a few more
56. 2:02intervals
57. 2:03you can clearly see the object is taking
58. 2:05a curved path
59. 2:07as the vertical velocity keeps on
60. 2:09decreasing as the ball travels up the
61. 2:11point where the vertical velocity
62. 2:13becomes zero will be the maximum height
63. 2:15it can achieve
64. 2:18after this point the vertical velocity
65. 2:20will become negative and the object will
66. 2:22start its descent
67. 2:24during the descent the gravitational
68. 2:26force and velocity are in the same
69. 2:28direction so the vertical velocity will
70. 2:30keep increasing
71. 2:32this will be the final shape traced by
72. 2:34the ball the shape of this trajectory is
73. 2:36known as a parabola
74. 2:39here's an interesting thought experiment
75. 2:42this cannon is ejecting a ball perfectly
76. 2:44vertically
77. 2:46the ball will come back to its initial
78. 2:47position or zero movement in the
79. 2:49horizontal direction
80. 2:51now let's reduce the angle and eject it
81. 2:53with the same speed now the ball can
82. 2:56travel horizontally
83. 2:57with a little more angle reduction the
84. 2:59range increases further when the
85. 3:02cannon's angle is down to 45 degrees the
86. 3:04range becomes even higher however if you
87. 3:07increase the angle after 45 degrees the
88. 3:10outcome is different the range actually
89. 3:13decreases
90. 3:14the maximum range is at an angle of 45
91. 3:17degrees before and after that the range
92. 3:19decreases
93. 3:20can you guess the reason behind this
94. 3:24the range of the ball is multiplication
95. 3:26of the initial horizontal velocity you
96. 3:28have given multiplied by the time
97. 3:30duration it stays in the air
98. 3:33the time the ball spends in the air
99. 3:34decreases as you decrease the angle
100. 3:42however the horizontal velocity keeps on
101. 3:44increasing as you reduce the angle
102. 3:48multiplication of two numbers will be
103. 3:50maximum when both the factors have a
104. 3:52good value
105. 3:53in this case the time the ball spent in
106. 3:55the air and horizontal velocity has a
107. 3:58good value at the angle of 45 degrees
108. 4:02this is why you get maximum range when
109. 4:04you throw the ball at 45 degrees
110. 4:08with this understanding of projectile
111. 4:10motion it becomes quite easy to solve
112. 4:12the question we posed at the beginning
113. 4:14of the video
114. 4:16the time it takes for the stone to hit
115. 4:18the ground depends only on its vertical
116. 4:20velocity even if you have given a high
117. 4:23horizontal velocity to your stone its
118. 4:25vertical component is zero this means
119. 4:28both the stones have the same vertical
120. 4:31component of velocity at the beginning
121. 4:33zero
122. 4:34this velocity will increase over time
123. 4:37due to the effect of gravity but with
124. 4:39the same magnitude
125. 4:41this means the vertical component of
126. 4:43velocity of both stones is the same
127. 4:46throughout their travel
128. 4:47therefore both will hit the ground at
129. 4:50the same time
130. 4:51pretty interesting right
131. 4:53the greater speed you have given to the
132. 4:54stone has no effect at all on its travel
133. 4:57time because you threw the stone
134. 4:59perfectly horizontally
135. 5:02thank you for watching we hope you
136. 5:04enjoyed the video
137. 5:06see you next time