he cannon on a battleship can fire a shell a maximum distance of 32.0 km. (a) Calculate

Physics Projectile Motion ­New equa2ions R(θ ) = Vo sinθ2)/g h= Vo^2 sin^2( θ ) / 2θ) 2 t= Vi ± √ −2gd+Vo / g ­Describe motion of object in 2 dimensions ­Ball is in free fall vertically and moves at a constant speed horizontally ­Force is in opposite direction to ball’s velocity vector and is proportional to the velocity at relatively low speeds ­Keep it simple by considering motion close to the surface of the earth for the time being ­Neglect air resistance to make it simpler ­An object falling is in free fall vertically and moves at a constant speed horizontally ­ What happens when we add air resistance Adds a new force on the ball ­The force is in the opposite direction to the ball’s velocity vector and is proportional to the velocity at relatively low speeds ­Need calculus to sort out the resulting motion ­Lowers the angle for maximum range The trick to maximum range is just to keep the object off the ground for as long as possible. ­This allows the horizontal motion to be a maximum since x = vxt ­Make range longer by going higher for your starting point ­Make range longer by having more velocity Communications Satellites ­Farther out you go, the bigger the circumference of the orbit ­It takes longer for the trip ­Also, gravity weakens by inverse square law the farther out you go ­Make the distance so that it takes 24 hours for the orbit ­Satellite is stationary in the sky!!! Kepler’s Laws ­Each planet moves in an elliptical orbit with the sun at one focus of the ellipse. ­The line from the sun t