A4-kilogram cat is resting on top of a bookshelf that is 3 meters high. what is the cat’s gravitational potential energy relative to the floor if the acceleration due to gravity is 9.8 m/s^2?

The roller coaster from problem #1 then tops a second hill at 15.0 m/s, how high is the second hill? 91.5 m 79.2 m 80.0 m 68.5 m

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)

An alpha particle with kinetic energy 12.5 mev makes a collision with lead nucleus, but it is not "aimed" at the center of the lead nucleus, and has an initial nonzero angular momentum (with respect to the stationary lead nucleus) of magnitude l = p0 b, where p0 is the magnitude of the initial momentum of the alpha particle and b=1.40×10−12 m. (assume that the lead nucleus remains stationary and that it may be treated as a point charge. the atomic number of lead is 82. the alpha particle is a helium nucleus, with atomic number 2.) what is the distance of closest approach?