Vectors Day 7 Lyzinski Physics

Day #7

A man is standing on a riverboat next to his wife A man is standing on a riverboat next to his wife. The boat is moving down a river without propelling itself, using only the current’s speed, which is 50 ft/min. The man starts jogging towards the front of the boat with a speed of 100 ft/min. During his jog, a smaller boat, traveling at 150 ft/min (relative to the water), passes the boat (in the same direction). A bird is sitting on the shore, watching the whole situation unravel. 150 ft/min  What is the man’s velocity (relative to the bird) when he is running? What is the man’s velocity (relative to his wife) when he is running? What is the man’s velocity (relative to the speedboat) when he is running? What is the wife’s velocity relative to the bird? What is the wife’s velocity relative to the speedboat? 100 ft/min  50 ft/min  50 ft/min  150 ft/min 

It depends on the “Frame of Reference” of the observer. So, what was the velocity of the man? It depends. What is the velocity relative to? It depends on the “Frame of Reference” of the observer.

Two cars are moving towards each other on a highway Two cars are moving towards each other on a highway. Car A moves East at 60 mph, while car B moves West at 50 mph. Find the velocity of car A with respect to …. a) car B b) a bird sitting on the side of the highway c) a boy in the backseat of car A 110 mph [E] 60 mph [E] 0 mph V AG = 60 mph V BG = 50 mph

In relative velocity problems, we often use what is known as a “relative velocity equation”. When you see a term like “VBC” this means “the velocity of the Ball relative to the Car” (for example)

The relative velocity equation vBS = vBC + vCS Here’s an easy trick to remember the equation vBS = vBS vB vBS + v S C C VBS = velocity of the ball relative to the side of the road VBC = velocity of the ball relative to the car VCS = velocity of the car relative to the side of the road

* REALLY IMPORTANT NOTE

VAB = VAG + VGB = + VAbird = VAG + VGbird = + VAboy = VAG + VGboy = + Looking at this problem again  Two cars are moving towards each other on a highway. Car A moves East at 60 mph, while car B moves West at 50 mph. Find the velocity of car A with respect to …. a) car B b) a bird sitting on the side of the highway c) a boy in the backseat of car A VAB = VAG + VGB = + 60 mph 50 mph 110 mph [E] 60 mph [E] VAbird = VAG + VGbird = + 60 mph 0 mph VAboy = VAG + VGboy = + 60 mph 60 mph

vBS = vBC + vCS vBS = vBC + vCS Example: A boy sits in his car with a tennis ball. The car is moving at a speed of 20 mph. If he can throw the ball 30 mph, find the speed with which he will could hit… his brother in the front seat of the car. b) A sign on the side of the road that the car is about to pass. c) A sign on the side of the road that the car has already passed 30 mph 50 mph vBS = vBC + vCS 30 mph 20 mph 10 mph 20 mph vBS = vBC + vCS 30 mph

River Problems

River Problems vCB = vCW + vWB Crossing a river: aiming straight across, but not accounting for the moving water  VCW = velocity of the canoe relative to the water (the velocity that the canoeist paddles) VWB = velocity of the water relative to the riverbank (the velocity of the river current) VCB = velocity of the canoeist relative to the riverbank vCB = vCW + vWB

VCW = velocity of the canoe relative to the water (the velocity that the canoeist paddles) VWB = velocity of the water relative to the riverbank (the velocity of the river current) VCB = velocity of the canoeist relative to the riverbank When answering any questions about going “ACROSS” the river, use the ACROSS THE RIVER Component. When answering any questions about going “DOWNSTREAM, use the DOWNSTREAM Component. The “slanted” vector is how the canoe will move from the perspective of anyone standing on the shore.

Example: A 20 m wide river flows at 1. 5 m/s Example: A 20 m wide river flows at 1.5 m/s. A boy canoes across it at 2 m/s relative to the water. a. What is the least time she requires to cross the river? b. How far downstream will she be when she lands on the opposite shore? c. What will her velocity relative to the shore be as she crosses? d = rt  20m = (2 m/s) t  t = 10 seconds. d = rt = (1.5 m/s)(10 sec) = 15 meters 2 1.5 2.5 2.5 m/s [across 36.87o downstream]

River Problems vGB = vGW + vWB Crossing a river: trying to go from point A to point B B VWB = velocity of the water relative to the riverbank (the velocity of the river current) VGB = velocity of the girl relative to the riverbank VGW = velocity of the girl relative to the water (the velocity that the girl swims) A vGB = vGW + vWB

Example: A river is 20 m wide. It flows at 1. 5 m/s Example: A river is 20 m wide. It flows at 1.5 m/s. If a girl swims at a speed of 2 m/s, find: a) the time required for the girl to swim 15 m upstream. b) the time required for the girl to swim 15 m downstream. c) the angle (between the swimmers path and the shore that the girl should aim when crossing the river if she wants to arrive at the other side directly across from her starting point. d = rt  15m = (2 m/s – 1.5 m/s)t  t = 30 seconds d = rt  15m = (2 m/s + 1.5 m/s)t  t = 4.29 seconds 2 1.5 1.32 q q q = cos-1 (1.5/2) = 41.4o [upstream 41.4o across]

From previous example: A river is 20 m wide. It flows at 1. 5 m/s From previous example: A river is 20 m wide. It flows at 1.5 m/s. The girl swims at a speed of 2 m/s. d) How long will it take to cross the river in this case (the case where the girl adjusts for the current by pointing herself upstream) d = rt  20m = (1.32 m/s)t  t = 15.2 seconds 2 1.5 1.32 q

“Day #7 Vectors HW Problems” (from the packet) Tonight’s HW “Day #7 Vectors HW Problems” (from the packet) #’s 36-44