Relative Velocity Practice + Special Relativity

Grab a reference table

Note: Answer all of these questions with respect to the spaceship.

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]

AP Equations

• In terms of position, not displacement (work backwards from regents to AP)

2-D Relative MotionContinued..

If you are confident, do this problem by yourself

If you have any doubt, follow along

2-D Relative MotionQ1. 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?

2-D Relative MotionQ1. 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?

Independence of vectors

X-component is separate from Y-component

2-D Relative MotionQ1. 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?

2-D Relative MotionQ1. 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?

When would you use the resultant velocity?

You tryQ1. 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

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) = 89.44 m NE

You tryQ2. 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.

You tryQ2. 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) = 32.35 º S of E or 32.35º + 270º = 302.35º

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

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

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 = √(dx2 + dy2) [as long as you don’t approximate]

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)