Newton's Law of Cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings (the ambient temperature). If we measure temperature in degrees Celsius and time in minutes, the constant of proportionality k equal 0.5. Suppose the ambient temperature TA(t) is equal to a constant 95 degrees Celsius. Write the differential equation that describes the time evolution of the temperature T of the object.

Abasketball star covers 2.65 m horizontally in a jump to dunk the ball. his motion through space can be modeled precisely as that of a particle at his center of mass. his center of mass is at elevation 1.02 m when he leaves the floor. it reaches a maximum height of 1.90 m above the floor and is at elevation 0.910 m when he touches down again. (a) determine his time of flight (his "hang time"). (b) determine his horizontal velocity at the instant of takeoff. (c) determine his vertical velocity at the instant of takeoff. (d) determine his takeoff angle. (e) for comparison, determine the hang time of a whitetail deer making a jump with center-of-mass elevations yi = 1.20 m, ymax = 2.45 m, and yf = 0.750 m.