Chapter 6Motion in Two Directions

Projectile MotionProjectile- object shot through the airTrajectory- the path that a projectile follows How can horizontal and vertical displacement be

determined?1. Vertical displacement

dy= ½gt2 + vit

if vi=0 then dy= ½gt2

2. Horizontal displacement

dx= vxt

Example

• A stone is thrown horizontally at 15m/s. It is thrown from the top of a cliff 44 m high.

a. How long does it take the stone to reach the bottom of the cliff?

b. How far from the base of the cliff does the stone strike the ground?

Example

A projectile is launched horizontally from the top of a building with a velocity of 12.7m/s. At what height is the projectile launched if the projectile lands 15.0 m from the side of the building?

Projectiles Launched at an Angle

• A golf ball is hit and leaves the tee with a velocity of 25.0 m/s at 35.0° with respect to the horizontal. What is the horizontal displacement of the ball?

V= 25.0 m/s= 35.0°

dx= ?t=?

Example

• A projectile is fired with a velocity of 19.6 m/s at an angle of 60.0° with the horizontal.

a. Calculate the vertical and horizontal velocity of the projectile.

b. Calculate the time the projectile is in the air.c. Determine the horizontal displacement that the

projectile travels.d. Determine the maximum height the projectile

reaches.

Circular Motion

• Centripetal acceleration

• - center-seeking acceleration of an object moving in a circle.

How is it determined?

Ac= v2/r or

Ac= 42r/T2

Centripetal Force

• Net force directed toward the center of a circle

How is it determined?

Fnet= mac

Example: A 13g rubber stopper is attached to a 0.93 m string. The stopper is swung in a horizontal circle, making one revolution in 1.18s. Find the tension force exerted by the string on the stopper.

Relative Velocity

• Motion is relative to an observer

• Example: A motor boat traveling 6.0 m/s, East encounters a current traveling 3.8 m/s, South.

a. What is the resultant velocity?b. If the width of the river is 120 m 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?