-- Bob covered a distance of (32m + 45m) = 77 meters.
-- His displacement is the straight-line distance and direction
from his starting point to his ending point.
The straight-line distance is
D = √(32² + 45²)
D = √(1,024 + 2,025)
D = √3,049 = 55.22 meters
The direction is the angle whose tangent is (32/45) south of east.
tan⁻¹(32/45) = tan⁻¹(0.7111...) = 35.42° south of east.
Answer:
The acceleration at the astronaut's head decreases.
Explanation:
Since the centripetal acceleration equals acceleration due to gravity,
a = g = GM/R². since a changes infinitesimally from his foot to his head, we differentiate a with respect to r to get da/dr = -2GM/R³.
So, da, the change in acceleration = -2GMdR/R³ = -2gdR/R = -2 × 9.8/6.4 × 10⁶ m = -3.0625 × 10⁻⁶dR m/s².
Since dR = height of astronaut = 1.80 m, da = -3.0625 × 10⁻⁶ × 1.8 = -5.5125 × 10⁻⁶ m/s².
So the acceleration at the astronaut's head is g + da = 9.8 - 0.0000055125 = 9.7999944875 m/s².
So the acceleration at the astronaut's head decreases.
911.1×155.9 = 14,202.49
14,202.49 in 3 significant figures would be either 14,200 or 1.42×10^4
