2.3 010 projectile_motion
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How does the horizontal and vertical motion differ on the x- and y-planes?
Horizontally…
Vertically…
Combined…
Combined…
Actual…
Motion Diagrams
Projectile MotionFor a projectile:
a) Describe the horizontal and vertical motion.
b) Describe the horizontal and vertical acceleration.
c) What equations would you use to calculate horizontal and vertical motion.
Horizontal constant velocity
Vertical accelerating
Horizontal zero
Vertical 9.8 m/s2
Horizontal v = d/t
Vertical v = at and d = ½ at2
Describe the horizontal motion of a projectile.
A projectile moves horizontally with constant velocity.
What is the horizontal acceleration for a projectile?
Horizontal acceleration is zero.
If you throw a projectile horizontally at a speed of 25 m/s, how fast will it be moving, horizontally, after 3 s?
Horizontally, it will still be moving at 25 m/s.
Horizontally…
Describe the vertical motion of a projectile.
Vertically, a projectile accelerates…
…at a rate of 9.8 m/s2
What happens, vertically, as a projectile
moves upward?
Vertically, a projectile slows down on the way up.
What happens, vertically, as a
projectile moves downward?
Vertically, a projectile speeds up on the way down.
If a projectile is thrown horizontally at a speed of 25 m/s, how fast is the projectile moving vertically after 3 s?
Vertically, the projectile will be moving 29.4 m/s.
Vertically…
So, if you throw a projectile horizontally at a speed of 25 m/s, how fast is it moving after 3 seconds?
Horizontally, it is moving at 25 m/s, vertically it is moving 30 m/s, so (by Pythagorean’s Theorem) the projectile is moving at 39 m/s.
25 m/s
30 m/sactual motion
0 vertical velocity
25 m/s
Initially…
After 3 s…
30 m/s39 m/s
25 m/s
Group Round 1 Round 2 Round 3
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Projectile motion problems…The key to solving problems involving
projectile motion is…• understanding that x and y are
independent.• identifying and separating x and y
variables.• understanding that time is the same
for both x and y.• Using appropriate equations for x
and y.
B4 stopped
Projectile motion problems…Useful tips… • Draw a picture.• Make a table with an x column
and a y column to identify variables.
• Immediately write down acceleration due to gravity (g) in the y column.
• Time connects x and y.
Projectile motion problems…Equations… • Along the x-axis:
– no acceleration; moves w/ constant velocity.
– v = d/t• Along the y-axis:
– Accelerates b/c of gravity; g = 9.8 m/s2.– v = at– d = ½at2
Lamp on a table…If I knock a lamp off an end-table with
a horizontal velocity of 5 m/s and the table is 0.5 meters high, how far away does the lamp land?
1.6 meters in front of table.
Kickin’ rocks…A rock is kicked horizontally off a cliff
and lands 125 meters in front of the cliff. If the cliff is 80 meters high, how fast is the rock initially kicked?
31.25 m/s horizontally.
B1 stopped
Tossing pennies…A penny is thrown horizontally of a building
with a velocity of 10 m/s. If the penny lands 78 meters in front of the building, how tall is the building?
It is 304.2 meters tall.
A2 stopped
Stranded on a mountain…An airplane traveling at 80 m/s
at an elevation of 250 m, drops a box of supplies to skiers stranded in a snowstorm. At what horizontal distance from the skiers should the supplies be dropped?
They need to be dropped 571.43 m before target (565.69 if using 10).
Stranded on a mountain…(con’t)
What is the speed of the box as it reaches the ground?
It is going 106.3 m/s (106.8 m/s if using 10)
Stone throw…Paco, standing on a cliff, throws a stone with a horizontal velocity of 15.0 m/s and the stone hits the ground 47.0 m from the base of the cliff. How high is the cliff?
The cliff is 48 m high.