he cannon on a battleship can fire a shell a maximum distance of 32.0 km. (a) Calculate the initial velocity of the shell. (b) What maximum height does it reach? (At its highest, the shell is above 60% of the atmospherebut air resistance is not really negligible as assumed to make this problem easier.) (c) The ocean is not flat, because the Earth is curved. Assume that the radius of the Earth is 6.37103 km . How many meters lower will its surface be 32.0 km from the ship along a horizontal line parallel to the surface at the ship? Does your answer imply that error introduced by the assumption of a flat Earth in projectile motion is significant here?

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