NASA engineers are designing a new spacesuit and must determine how quickly an a
ID: 2059644 • Letter: N
Question
NASA engineers are designing a new spacesuit and must determine how quickly an astronaut can walk. The length of time T between steps depends on the length L of the step and the acceleration due to gravity g through a relationshipT = ßLagb for some constant ß and exponents a, b.They've performed 3 experiments on Earth (g = 9.8 m/s2) and on the Moon (g = 1.6 m/s2) with the following results:
1. g = 9.8 m/s2, L = 1.0 metre, T = 2.01 seconds
2. g = 9.8 m/s2, L = 0.5 metres, T = 1.42 seconds
3. g = 1.6 m/s2, L = 1.0 metre, T = 4.97 seconds
Determine the values of the exponents a, b and the constant ß:
Explanation / Answer
Given, T= *L^a*g^b
Putting values from 3 experiments, we get the following 3 equations:
2.01 = *1^a*9.8^b
1.42 = *0.5^a*9.8^b
4.97 = *1^a*1.6^b
solving these 3 equations, we get =6.29, a= 0.5, b= -0.5
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