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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