Non-Horizontally Launched Projectiles

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Presentation transcript:

Non-Horizontally Launched Projectiles Fired at an angle… Have some Velocity in each direction There is some velocity in the x-direction And some velocity in the y - direction Vy = vertical velocity Vx = horizontal velocity

Non-Horizontally Launched Projectiles Shot @ 30 degrees Shot @ 60 degrees Shot closer to horizontal So horizontal velocity greater than vertical velocity Vx > Vy Shot closer to vertical So vertical velocity greater than horizontal velocity Vv > Vx Vy Vy Vx Vx

Non-Horizontally Launched Projectiles Angle for Max Time in the Air? Time in the air only affected by vertical direction Launch angle should maximize velocity in the vertical direction Launch angle for max time in the air – 90 degrees Vy = maximum amount Vx = 0 !! All velocity is in the y-direction No velocity in the x

Non-Horizontally Launched Projectiles Maximum Range – max horizontal displacement dx must be the biggest number So we want Vx and time to be the biggest number possible… But remember… Range, dx = Vx * time of flight

Non-Horizontally Launched Projectiles Maximum Range – max horizontal displacement dx must be the biggest number So we want Vx and time to be the biggest number possible… But remember… If launch angle is zero – 0 – then… Vx is at a maximum but time of flight is at a minimum Range, dx = Vx * time of flight

Non-Horizontally Launched Projectiles Maximum Range – max horizontal displacement dx must be the biggest number So we want Vx and time to be the biggest number possible… So which is more important? Horizontal Vx or vertical time of flight ? Neither!! Max Range is at 45 degrees!! Why??? Range, dx = Vx * time of flight

Non-Horizontally Launched Projectiles Maximum Range – max horizontal displacement At 45 degrees Vx = Vy Most of Vx and time Of flight Without sacrificing one for the other Range, dx = Vx * time of flight

Non-Horizontally Launched Projectiles Relationship between 30/60 and 15/75 30/60 (and 15/75) have equal displacements because… Range, dx = Vx * time of flight

Non-Horizontally Launched Projectiles Shot @ 30 degrees Shot @ 60 degrees Shot closer to horizontal Vx of 30 degrees = Vy of 60 degrees and… Vx of 60 degrees = Vy of 30 degrees… So… ratio of Vx and time of flight is the same dx is the same! Shot closer to vertical Vy Vy Vx THEY ARE THE SAME TRIANGLE!!!! Vx