Projectile Motion and Circular Motion Notes, Study notes of Physics

Download Projectile Motion and Circular Motion Notes and more Study notes Physics in PDF only on Docsity! Ch 4 notes (2/2) Projectile motion (special case, cont’d) Circular motion Relative motion Projectile motion: f(t) 0 0 0 2 0 0 0 0 1 2 x x x x y y y y a v v x x v t a g v v gt y y v t gt = = = + = − = − = + − NOTE: motion along x does NOT depend on y, vy, ay and wise versa Projectile motion: Range 02 0 0 0 2 2 0 0 0 0 0 Range: 0 1 0 2 2 2 2cos sin sin 2 y y y x y v v t gt t g v Range v g v v g g θ θ θ = − = → = ⎛ ⎞ = =⎜ ⎟ ⎝ ⎠ = = x y Range 0 2 0 1 2 x y x v t y v t gt = = − θ0=0° Range=0 θ0=90° Range=0 θ0=45° Max Range Example monkey gun Blue ball (target) is released when red cannonball emerges from cannon. Geometry is given. Find the required velocity to hit the target. Example A cannon on your ship can eject a cannonball at speed v, at what angle you need to aim in order to hit a pirate ship at distance d. Circular Motion (3) α x y 2 2 2 2 2 ˆ ˆ( cos ) ( sin ) ˆ ˆ( sin ) ( cos ) ˆ ˆ( cos ) ( sin ) r r t i r t j drv r t i r t j dt dva r t i r t j dt a r va r const r ω ω ω ω ω ω ω ω ω ω ω ω = + = = − + = = − + − = − = = = centripetal acceleration (m/s2) points to center r Example A pilot is tested in a centrifuge of radius 5 m. The centrifuge makes 20 turns per min. What is the centripetal acceleration experienced by the pilot? Relative motion ABr OBr x y OAr -- position of object O in coordinate system A -- position of coordinate system A origin in coordinate system B -- position of object O in coordinat OA AB OB r r r e system B OB AB OA OB OAAB OB AB OA r r r dr drdr v v v dt dt dt = + = + → = + Blue – coordinate system A Yellow – coordinate system B