Wednesday 5/27PHYS 2010

Nathalie HoffmannUniversity of Utah

Relative Velocity

• (read as: velocity of object A with respect to object C equals velocity of A with respect to B plus velocity of B with respect to C)

• (velocity of object A with respect to B equals the negative of the velocity of B with respect to A)

• For example:

Projectile motion

• Acceleration (in y direction) due to gravity

• Constant velocity in x direction (

• Parabolic trajectory

Kinematics Equations for Projectile Motion• Constant acceleration in y direction

• alternatively, • alternatively,

• Note: when , then above should be

Simplified version

• Y direction (

• X direction•

Practice Problems• An object undergoing parabolic motion travels 100 m in the horizontal

direction before returning to its initial height. If the object is thrown initially at a 30° angle from the horizontal, determine the x component and the y component of the initial velocity. (Neglect any effects due to air resistance.)

• A spider crawling across a table leaps onto a magazine blocking its path. The initial velocity of the spider is 0.870 m/s at an angle of 35.0° above the table, and it lands on the magazine 0.0770 s after leaving the table. Ignore air resistance. How thick is the magazine? Express your answer in millimeters.

• The president’s airplane, Air Force One, flies at 250 m/s to the east with respect to the air. The air is moving at 35 m/s to the north with respect to the ground. Find the velocity of Air Force One with respect to the ground.

Practice Problems• Two boats are heading away from shore. Boat 1 heads due north at a speed of 3.00

m/s relative to the shore. Relative to boat 1, boat 2 is moving 30.0 north of east at a speed of 1.60 m/s. A passenger on boat 2 walks due east across the deck at a speed of 1.20 m/s relative to boat 2. What is the speed of the passenger relative to the shore?

• Mario, a hockey player, is skating due south at a speed of 7.0 m/s relative to the ice. A teammate passes the puck to him. The puck has a speed of 11.0 m/s and is moving in a direction of 22° west of south, relative to the ice. What are the magnitude and direction (relative to due south) of the puck's velocity, as observed by Mario?

• In the aerials competition in skiing, the competitors speed down a ramp that slopes sharply upward at the end. The sharp upward slope launches them into the air, where they perform acrobatic maneuvers. The end of a launch ramp is directed 63° above the horizontal. With this launch angle, a skier attains a height of 13 m above the end of the ramp. What is the skier's launch speed?

Practice Problem Answers

• P1.1: vx = 29.13 m/s, vy = 16.82 m/s• P1.2: Thickness = 9.4 mm• P1.3: • P2.1: • P2.2: at 52° west of south• P2.3: v = 18 m/s