To solve this problem, we can use the cosine formula for
calculating the length of the displacement:
c^2 = a^2 + b^2 – 2 a b cos θ
where c is the displacement, a = 3.5 km, b = 4.5 km, and θ
is the angle inside the triangle
Since the geeze turned 40° from west to north, so the
angle inside the triangle must be:
θ = 180 – 40 = 140°
c^2 = 3.5^2 + 4.5^2 – 2 (3.5) (4.5) cos 140
c^2 = 56.63
c = 7.53 km
<span>So the magnitude of the displacement is 7.53 km</span>
I believe the correct answer is d. thermosphere.
Solution:
a) We know acceleration due to gravity, g = GM/r²
Differential change, dg/dr = -2GM/r³
Here, r = 50*Rh = 50*2GM/c² = 100GM/c
²
My height, h=dr = 1.7 m
Difference in gravitational acceleration between my head and my feet, dg = -10 m/s²
or, dg/dr = -10/1.7 = -2GM/(100GM/c²)³
or, 5.9*100³*G²*M² = 2c⁶
or, M = 0.59*c³/(1000G) = 2.39*1032 kg = [(2.39*1032)/(1.99*1030 )]Ms = 120*Ms
Mass of black hole which we can tolerate at the given distance is 120 time the mass of Sun.
b) This limit an upper limit ,we can tolerate smaller masses only.
