Constant Acceleration and Relative Velocity

Relative Velocity Sometimes your velocity is known relative to a reference frame that is moving relative to the earth. Example 1: A person moving relative to a train, which is moving relative to the ground. Example 2: a plane moving relative to air, which is then moving relative to the ground. These velocities are related by vector addition: vac is the velocity of the object relative to the ground vab is the velocity of the object relative to a moving reference frame vbc is the velocity of the moving reference frame relative to the ground 32

Relative Velocity You are on a train traveling 40 mph North. If you walk 5 mph toward the front of the train, what is your speed relative to the ground? A) 45 mph B) 40 mph C) 35 mph 40 5 45 25

Relative Velocity You are on a train traveling 40 mph North. If you walk 5 mph toward the rear of the train, what is your speed relative to the ground? A) 45 mph B) 40 mph C) 35 mph 40 5 35 27

Relative Velocity You are on a train traveling 40 mph North. If you walk 5 mph sideways across the car, what is your speed relative to the ground? A) < 40 mph B) 40 mph C) >40 mph 40 mph N + 5 mph W = 5 40 30

Example: airplane An airplane needs to fly due south to reach it’s destination, but there is a wind blowing from the east. Will this increase, decrease or have no effect on the travel time? vp= 50 m/s vT vw= 20 m/s

x y Example Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Relative to the water, Beth (B) swims perpendicular to the flow, Ann (A) swims upstream, and Carly (C) swims downstream. Which swimmer wins the race? A) Ann B) Beth C) Carly correct Add Calculation. What angle to get straight across river? A B C 39

x y Example If the width of the river is 50m and Beth can swim at 3m/s, how long does it take her to get across? If the river is flowing at 2m/s, How far downstream is she swept? A B C 2m/s 50m Add Calculation. What angle to get straight across river? 39

x y Swimmer Example What angle should Ann take to get directly to the other side if she can swim 3 mph relative to the water, and the river is flowing at 2 mph? How long does it take her to get across? q Add Calculation. What angle to get straight across river? 36.8 degrees A B C 2m/s 48

Summary of Concepts X and Y directions are Independent! Position, velocity and acceleration are vectors F = m a applies in both x and y direction Relative Motion (Add vector components)