On Planet X, an astronaut has maximum walking speed of 1.9 m/s. The astronaut's legs are each 1.3 m long. What is the constant of acceleration due to gravity on Planet X?
To find the constant of acceleration due to gravity on Planet X, we can use the relationship between the walking speed and leg length of the astronaut.
On Earth, the relation between walking speed (v) and leg length (L) is given by:
v = √(g * L)
where g is the acceleration due to gravity on Earth (approximately 9.8 m/s^2).
However, on Planet X, we need to find the acceleration due to gravity (gX). The relationship between walking speed and leg length will be the same, so we can write it as:
vX = √(gX * L)
We are given that the maximum walking speed of the astronaut is 1.9 m/s and the leg length is 1.3 m. Plugging these values into the equation, we get:
1.9 = √(gX * 1.3)
To solve for gX, we need to square both sides of the equation:
1.9^2 = (gX * 1.3)^2
3.61 = gX^2 * 1.69
Dividing both sides by 1.69:
2.1396 = gX^2
Taking the square root of both sides, we find:
gX ≈ √2.1396
Therefore, the constant of acceleration due to gravity on Planet X is approximately 1.462 m/s^2.