You are testing a new roller coaster ride in which a car of mass m moves around a vertical circle of radius r. in one test, the car starts at the bottom of the circle (point a) with initial kinetic energy ki. when the car reaches the top of the circle (point b), its kinetic energy is ki/4, and its gravitational potential energy has increased by ki/2. what was the speed of the car at point a, in terms of g and r?

Basilisk lizards can run across the top of a water surface (see the figure). with each step, a lizard first slaps its foot against the water and then pushes it down into the water rapidly enough to form an air cavity around the top of the foot. to avoid having to pull the foot back up against water drag in order to complete the step, the lizard withdraws the foot before the water can flow into the air cavity. if the lizard is not to sink, the average upward impulse on the lizard during this full action of slap, downward push, and withdrawal must match the downward impulse due to the gravitational force. suppose the mass of a basilisk lizard is 93.7 g, the mass of each foot is 3.37 g, the speed of a foot as it slaps the water is 1.15 m/s, and the time for a single step is 0.531 as. (a) what is the magnitude of the impulse on the lizard during the slap