Question

11 In the 1964 Olympics in Tokyo, the best men's high jump was 2.18 m. Four years later in Mexico City, the gold medal in the same event was for a jump of 2.24 m. Because of Mexico City's altitude (2400 m), the acceleration of gravity there is lower than that in Tokyo by about 0.01 m/s?. Suppose a high-jumper has a mass of 72 kg (a) Compare his mass and weight in the two locations. (b) Assume that he is able to jump with the same initial vertical velocity in both locations, and that all other conditions are the same except for gravity. How much higher should he be able to jump in Mexico City? (Actually, the reason for the big change between 64 and '68 was the introduction of the "Fosbury flop.")

Answer 1

I Tokyo mass will remain same irrespectue of location ie m= 72kg on both locations. It Tokyo g, = 9.81 m/s² weight W, = mg, = 7249.81 = 706.32 N At Mexico City g = 9.8 m/s² { less than by 0:01 m/s that in) . Wz= mga = 72x98 = 705.6N 2 W, JWz , Weight force of the person is greater in a Tokyo than in Mexico City. ' (b) Let : che jumps with initial velocity to on both places Let he reached ho, height in Tokyo 3 mg, hi = 1 m2 - 4x = h, - postential energy = Kinectic energy Ilaw of conservatim genergy). In Mexico lity he reached the height 3 mgaha = 1 me? in a hea - from 0 a ③ we get - hz=g hi for g, = 9.81 m/s2, Gz = 9.8 m/s2 the = 9.81 h = 1.001 hi 9.8 =>" hz hi.