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Chapter 5 Projectile motion. Chapter 4: straight line motion that was ONLY vertical or ONLY horizontal motion. Chapter 5: considers motion that follows a diagonal path or a curved path. When you throw a baseball, the trajectory is a curved path.
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Chapter 4: straight line motionthat was ONLY vertical or ONLY horizontal motion
Chapter 5: considers motion that follows a diagonal path or a curved path
We are going to separate the motion of a projectile into independent x and y motions
The vertical motion is not affected by the horizontal motion. And the horizontal motion is not affected by the vertical motion.
Observe: a large ball bearing is dropped at the same time as a second ball bearing is fired horizontally.
Remember adding 2 perpendicular vectorshorizontal and vertical vectors.
When we add perpendicular vectors we use Pythagorean theorem to find the resultant.
Consider a vector B that is pointed at an angle q wrt horizontal direction.
We are going to break vector B into 2 perpendicular vectors: Bx and By
Draw a rectangle with vector B as the diagonal. the component vectorsBx and By are the sides of the rectangle
The motion is affected by the motor of the boat and by the current of the river
If a boat is placed in the river [motor is off] , how fast will the boat drift downstream?
If the boat is drifting, the total speed of the boat just equals the speed of the current.
for a boat drifting with the current: Vtotal= Vboat + VcurrentVtotal = -0 + Vcurrent = 8 m/sec
Now suppose this boat can travel at a constant 15 m/sec when the motor is on .
What is the total speed of the boat downstream when the motor is on?
V total downstream = Vtotal = Vboat + VcurrentVtotal = 15↓ + 8↓ = 23 m/sec ↓
What is the total speed of the boat traveling upstream[against the current] ?
Vtotal = Vboat +VcurrentVtotal = 15 ↓+ ( 8 ↑) Vtotal = 7↓ m/sec
Summary:traveling downstream: Vboat + VcurrentTraveling upstream:Vboat + [-Vcurrent]
If there was no current, how many seconds needed for this boat to travel 120 meters from A to B?
time = distance velocitytime = 120 m 15 m/sectime = 8 seconds
But there if IS a current. what happens when you try to go straight across the river from A to B?
Every second the boat travels ACROSS 15 meters and AT THE SAME TIMEevery secondthe boat will be pushedDOWNSTREAm 8 meters by the current .
Vboat = 15 and Vcurrent = 8↓These velocities are perpendicular
Vresultant2 = Vboat2 + Vcurrent2Vresultant2 = 152+ 82Vresultant2 = 225+ 64 =289Vresultant = 17 m/sec
The boat still crosses the river in 8 seconds , but it lands downstream at point C not at point B.