Kinematics in 2D…

Projectile Motion

Think About It…

• What happens when you are driving at a constant speed and throw a ball straight up in the air? How does it look to a passenger in the car? How does it look to an observer on the side of the road?

Think About It…

• Consider a gun that could “drop” a bullet from the end of the muzzle at the same instant that a bullet was fired from the end of the muzzle. Which would hit the ground first?

Motion in 2D…• Consider a spaceship traveling

at constant speed. It has thrusters that are pointed both vertically and horizontally.• What happens when it fires the

vertical thruster?• What happens when it fires the

horizontal thruster?• What happens when it fires BOTH

thrusters at the same time?

Motion in 2D…

• Projectile Motion is defined as motion in two dimensions where the only external force acting on the system is gravity…

Motion in 2D…

•What examples of projectile motion can you think of from your experience (think about sports…)

Motion in 2D…

•When an object is in projectile motion, the motion in the x and y directions are INDEPENDENT of each other!

Motion in 2D…

•Fire/Drop a bullet demo•Throw a ball on a moving truck demo

•Monkey shooting

Time for a little gaming…

•Asteroids

•Pocket Tanks

Equations ofProjectile Motion

tavv xxx 0

tvvx xx 02

1

20 2

1tatvx xx

xavv xxx 220

2

tavv yyy 0

tvvy yy 02

1

20 2

1tatvy yy

yavv yyy 220

2

Using the Equations of Kinematics

• Choose positive x & y directions• Draw a picture• Make a chart of initial conditions for

one or both directions• Choose equations to solve for the

unknown• Solve and check answer for

reasonability

Example #1A rocket’s engines fire to give it a constant acceleration in the x-direction of 24m/s2, and at the same time a constant acceleration in the y-direction of 12m/s2. After a certain amount of time the components of velocity are v0x=22m/s and v0y=14m/s. Find x, y, vx, and vy 7.0s later. Then find the velocity and displacement.

x=740mvx=190m/sy=390mvy=98m/sv=210 m/s @ 27° above x axis

Example #1

Example #2A UN aircraft flies over Kabul, Afghanistan to drop supplies. The plane has a velocity of 115m/s east (horizontally) and an altitude of 1050m. Determine the time it takes for a dropped supply box to reach the ground and the horizontal distance it will travel in the air (range).

t=14.6sx=1680m

Example #2

When fired from the ground, what angle will yield the maximum range for a projectile fired with initial speed v0?

Maximum range

Relative Velocity

• Describe the motion of a car moving at a constant speed of 50mph from three points of view:• The driver• A person waiting for a bus• A person in a car moving toward

the first car at 30mph

Relative Velocity

All motion must be describedwith respect to (w.r.t.) some

frame of reference

Usually the f.o.r. is assumed to be the stationary Earth

Relative Velocity

•Notation: v12

• the first subscript represents the body in question, the second represent the frame of reference.

• VAB represents the “speed of object A from the point of view of object B.”

Relative Velocity in 2D

• A police car travels North on Maple road at 45mph. If you are going 50mph East on Textile road, what velocity would the police radar gun clock you at?

• We have to use vector addition to find our answer…

Relative Velocity in 2D

• A boat can travel at 30.0mph in still water, how fast can it move crossing a river with current of 10mph? What is its velocity? How long will it take to cross a river 0.500 miles wide?

The End…