1-2-4 Horizontal Projectiles

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Horizontal Projectiles

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Presentation transcript:

1-2-4 Horizontal Projectiles Over the Edge 1-2-4 Horizontal Projectiles

A red ball rolls off the edge of a table What does its path look like as it falls? Parabolic path

As the red ball rolls off the edge, a green ball is dropped from rest from the same height at the same time Which one will hit the ground first? They will hit at the SAME TIME!!!

The same time?!? How?!? The green ball falls from rest and has no initial velocity IN EITHER DIRECTION! viy and vix = 0 The red ball has an initial HORIZONTAL velocity (vix) But does not have any initial VERTICAL velocity (viy = 0) vix

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

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

Need time from vertical Example #2 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

Need time from vertical Example #3 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 #4 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.