PHYSICS 103: Lecture 4
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Transcript of PHYSICS 103: Lecture 4
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PHYSICS 103: Lecture 4
• Freely falling objects Throwing a ball upward
• Projectile Motion Trajectory of projectile Hitting a target
• Freely falling objects Throwing a ball upward
• Projectile Motion Trajectory of projectile Hitting a target
Agenda for Today:
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A ball thrown upward returns to the ground. What are the magnitude and direction of the velocity at different points of the flight?
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The velocity vectors at different points in the flight of a ball thrown upward with a starting velocity of +20 m/s.
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Example: How high up can the fastest pitcher throw a ball? How long would it be in the air?
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PROJECTILE MOTION
Question: If I throw a ball horizontally, what happens?
How long does it take to hit the ground?
Does this depend on the speed with which I throw it?
If I throw a ball horizontally while simultaneously dropping one which hits the ground sooner?
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FREE FALL
Acceleration
Constant Motion(no acceleration)
dhorizontal = d0 + v0t dhorizontal = d0 + v0t range
dvertical = v0yt + 1/2gt2 dvertical = v0yt + 1/2gt2 height
Horizontal and Vertical Motion are Independent
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The horizontal and vertical motions combine to produce the trajectory of the projected ball.
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The total velocity at any point is found by adding thevertical component to the horizontal component.
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Trajectories for different initial velocities of a ball rolling off a table: v3 is larger than v2, which in turn is larger than v1.
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PROJECTILE MOTION
Example: Throwing a ball at an angle from a hilltopWhat is the distance down range from the base of a
hill 30 m high if a ball is thrown up at a 50o angle above the horizontal at 40 m/s? What is the time of flight? What is the maximum height?
Range = R
initial
horizontal motion
vertical
motion
final
50o
y
x
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To calculate the downrange distance, we need to calculate the time the ball is in the air. The time is determined from vertical (y) motion.
v0
v0x
v0y
50o
Example: Throwing a ball at an angle from a hilltop
v0y = v0 sin50o
Once we know the time in the air, we can calculate how far down range it will travel in that amount of time.
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Main Points from Today’s Lecture
• Throwing an object upwards You should know how to find out how high
up it will go, and how long it stays in the air
• Projectile Motion You should understand that the horizontal and
vertical motion for a projectile are independent You should be able to calculate how far down
range a projectile will travel if it is thrown at a given speed and angle
• Throwing an object upwards You should know how to find out how high
up it will go, and how long it stays in the air
• Projectile Motion You should understand that the horizontal and
vertical motion for a projectile are independent You should be able to calculate how far down
range a projectile will travel if it is thrown at a given speed and angle
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HW
Q8, Q10, Q11, Q12, Q14, Q16, Q17, Q23*, Q23*, Q25, Q26, E3, E7, E8,
E11, E13