To achieve the maximum benefit for the heart when exercising, the heart rate (in beats per minute) should be in the target heart rate zone. the lower limit of this zone is found by taking 70% of the difference between 220 and the age of the person. the upper limit is found by using 85% of the difference. find formulas for the upper and lower limits (u and l) as linear equations involving the age x.

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.