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to win the game, a place kicker must kick a football from a point 45 m (49.212 yd) from the goal, and the ball must clear the crossbar, which is 3.05 m high. when kicked, the ball leaves the ground with a speed of 24 m/s at an angle of 32.6 ◦ from the horizontal. the acceleration of gravity is 9.8 m/s 2 . by how much vertical distance does the ball clear the crossbar? answer in units of m.

Consider a small frictionless puck perched at the top of a fixed sphere of radius r. if the puck is given a tiny nudge so that it begins to slide down, through what vertical height will it descend before it leaves the surface of the sphere? [hint: use conservation of energy to find the puck's speed as a func e conservation of energy to find the puck's speed as a function of its height at what value of this normal force does the puck leave the sphere? ] here on the puck.