Answer:
V = 49.05 [m/s]
Explanation:
We can easily find the result using kinematics equations, first, we will find the distance traveled during the 5 seconds.

where:
Yo = initial position = 0
y = final position [m]
Vo = initial velocity = 0
t = time = 5 [s]
g = gravity aceleration = 9.81 [m/s^2]
The initial speed is zero, as the body drops without imparting an initial speed. Therefore:
y = 0 + (0*5) + (0.5*9.81*5^2)
y = 122.625[m]
Now using the following equation we can find the speed it reaches during the 5 seconds.
![v_{f} ^{2}= v_{i} ^{2}+(2*g*y)\\v_{f}=\sqrt{2*9.81*122.625} \\v_{f}=49.05 [m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%20%5E%7B2%7D%3D%20v_%7Bi%7D%20%5E%7B2%7D%2B%282%2Ag%2Ay%29%5C%5Cv_%7Bf%7D%3D%5Csqrt%7B2%2A9.81%2A122.625%7D%20%5C%5Cv_%7Bf%7D%3D49.05%20%5Bm%2Fs%5D)
spray him in the eyes and you have until he washes it put
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.