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Projectile Motion Physics 12

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Motion in 2D We are now going to investigate projectile motion where an object is free to move in both the x and y direction

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What is projectile motion? Any object given an initial thrust and then allowed to soar through the air under the force of gravity only is called a projectile.

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Projectile Motion We know that an object (in the absence of air resistance) that is launched at a given angle should follow a parabolic path

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Projectile Motion – Horizontal Launch An object that is launched horizontally will have no initial velocity in the y direction so the entire initial velocity will be in the x direction At this point, we are able to treat the projectile using our two equations of motion

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Parts of a Projectile Path Horizontal Distance = range Height of projectile = altitude, peak

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2D Motion of a Horizontal Thrust Gravity ONLY affects the vertical distance travelled Gravity is the ONLY force affecting the object (neglect air resistance) So a x = a y = v iy = 0 as there is no initial thrust given

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Projectile Motion - Equations

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Projectile Motion

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Projectile Motion Problem A cannonball is fired horizontally from the top of a 50.m high cliff with an initial speed of 30.m/s. Ignoring air resistance, determine the following: How long it takes to strike the ground How far from the base of the cliff it strikes the ground How fast it is travelling when it strikes the ground

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Projectile Motion Problem Start with y position equation (4) Sub in known information (h=50.m) and solve for time

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Projectile Motion Problem Now use x position equation (2) Sub in time and known information (t=3.2s, v ox =30.m/s) and solve for d x

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Projectile Motion Problem Finally we will use equations (1) and (3) Sub in time and solve for velocity

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Projectile Motion Problem Now, we employ trigonometry and Pythagorean Theorem to solve for the final velocity vxvx vyvy vrvr

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Example 2 You throw a rock off a 291m high cliff horizontally at 12.8 m/s. A) If the river below is 68.5 m wide, will the rock make it across the river? (98.6m so it will make it across) B) With what velocity will the rock hit the water/ground? (76.6 m/s [80.4’])

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Projectile Motion http://videolectures.net/mit801f99_le win_lec04/ http://videolectures.net/mit801f99_le win_lec04/ Page 536-7, questions 1 to 8

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