Ν τν τ a cannon shoots a cannon ball horizontally off a cliff at 650 m/s. what is its initial...
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ν τ
• A Cannon shoots a cannon ball horizontally off a cliff at 650 m/s.
• What is its initial vertical velocity?
• The cliff is 45 m high.
• How far did the cannon ball go?
• Hold on to your Homework for now
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Objectives
• Practice with Horizontally Launched Projectiles !!
• Unit Test Tomorrow on all Motion !!
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Homework
• Castle Learning – Horizontal Motion and Review !
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Over the Edge1-2-4 Horizontal Projectiles
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A red ball rolls off the edge of a table
What does its path look like as it falls?
Parabolic path
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As the red ball rolls off the edge, a greenball is dropped from rest from the same
height at the same time
Which one will hit the ground first?
They will hitat the SAME
TIME!!!
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The same time?!? How?!?
vix
The red ball has an initialHORIZONTAL velocity (vix)
But does not have any initialVERTICAL velocity (viy = 0)
The green ball falls from restand has no initial
velocity IN EITHERDIRECTION!
viy and vix = 0
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One Dimension at a Time
• Both balls begin with no VERTICAL VELOCITY
• Both fall the same VERTICAL DISTANCE
• This means that the time of flight IS THE SAME IN BOTH CASES
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Example #1 (not in notes)• A bullet is fired horizontally from a gun that is 1.7
meters above the ground with a velocity of 55 meters per second.
• At the same time that the bullet is fired, the shooter drops an identical bullet from the same height.
• Prove that the two bullets hit the ground at the same time.
For both bullets…
vi = 0
a = -9.81 m/s2
d = -1.7 m
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• An airplane making a supply drop to troops behind enemy lines is flying with a speed of 300 meters per second at an altitude of 3.0 kilometers.
– How far from the drop zone should the aircraft drop the supplies?
Need time from vertical
d = vit + ½ at2
3000 m = 0 + ½ (-9.81 m/s2)t2
t = 24.7 s
Use time in horizontal
d = vit + ½ at2
d = (300 m/s)(24.7 s) + 0
d = 7410 m
Example #2
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• A stuntman jumps off the edge of a 45 meter tall building to an air mattress that has been placed on the street below at 15 meters from the edge of the building.
– What minimum initial velocity does he need in order to make it onto the air mattress?
Need time from vertical
d = vit + ½ at2
45 m = 0 + ½ (-9.81 m/s2)t2
t = 3.03 s
Use time to find v
v = d / t
v = 15 m / 3.03 s
v = 4.95 m /s
Example #3
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• An astronaut on the Moon throws a wrench horizontally with a speed of 0.5 meters per second from a height of 1.5 meters. The astronaut simultaneously drops a feather from the same height. Which object will hit first? Why?
With no air resistance and identical vertical variables they hit the
ground at the same time.
Example #4
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New Dow