Relative Velocity Practice + Special Relativity. Grab a reference table
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1 Relative Velocity Practice + Special Relativity Grab a reference table
2 Note: Answer all of these questions with respect to the spaceship.
3
4 Announcements Lab Report is due Friday (Late = 55, No submission = 0) Tutorial videos are posted for excel (the first 2 are relevant for this lab, but knowing the information on all 4 will be as much excel as you need for the year) There is a data analysis component on the AP Exam 5 people aren t signed up for Quest and HW1 is going up on Friday [either registered incorrectly or haven t registered]
5 AP Equations In terms of position, not displacement (work backwards from regents to AP)
6 2-D Relative Motion Continued..
7 If you are confident, do this problem by yourself If you have any doubt, follow along
8 2-D Relative Motion Q1. A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, North. a. What is the resultant velocity of the motor boat (including angle)? b. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? c. What distance downstream does the boat reach the opposite shore?
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10 2-D Relative Motion Q1. A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, North. a. What is the resultant velocity of the motor boat (including angle)? b. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? c. What distance downstream does the boat reach the opposite shore?
11 Independence of vectors X-component is separate from Y-component
12 2-D Relative Motion Q1. A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, North. a. What is the resultant velocity of the motor boat (including angle)? b. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? c. What distance downstream does the boat reach the opposite shore?
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14 2-D Relative Motion Q1. A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, North. a. What is the resultant velocity of the motor boat (including angle)? b. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? c. What distance downstream does the boat reach the opposite shore?
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16 When would you use the resultant velocity?
17 You try Q1. A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, North. a. What is the resultant velocity of the motor boat? b. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? c. What distance downstream does the boat reach the opposite shore? d. Find the boats resultant displacement
18 When is the resultant velocity useful? d. Find the boats resultant displacement The boat traveled at a rate of 5.59 m/s for 16 s, so the displacement: d = vr*t = ( 5.59m/s)( 16s) = m NE
19 You try Q2. A motorboat traveling 6 m/s, East encounters a current traveling 3.8 m/s, South. a. What is the resultant velocity of the motor boat? b. The boat travels for 20s. How wide is the river? c. What distance downstream does the boat reach the opposite shore? d. Find the total displacement.
20 You try Q2. A motorboat traveling 6 m/s, East encounters a current traveling 3.8 m/s, South. a. What is the resultant velocity of the motor boat? Vr = sqrt((6m/s)^2 + (3.8 m/s)^2) = 7.1 m/s tan(ø) = (3.8/6) ø = tan-1 (3.8/6) = º S of E or 32.35º + 270º = º
21 You try Q2. A motorboat traveling 6 m/s, East encounters a current traveling 3.8 m/s, South. b. The boat travels for 20s. How wide is the river? t = 20s, d =?, Vx = 6m/s v = dx/t dx = 120m
22 You try Q2. A motorboat traveling 6 m/s, East encounters a current traveling 3.8 m/s, South. c. What distance downstream does the boat reach the opposite shore? t = 20s, dy =?, vy = 3.8 m/s dy = vy*t dy = 76m
23 You try Q2. A motorboat traveling 6 m/s, East encounters a current traveling 3.8 m/s, South. d. Find the total displacement. dr =?, vr = 7.1 m/s, t = 20s dr = vr*t = 142m Fun fact: dr = (dx 2 + dy 2 ) [as long as you don t approximate]
24 Extension: Special Relativity Not part of AP curriculum Derived from Maxwell s equations Everything is relative, except c Time dilation and Length contraction Only relevant for really fast things (significant portions of the speed of light)
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