(1) You must find the point of equilibrium between the two forces,
<span>G * <span><span><span>MT</span><span>ms / </span></span><span>(R−x)^2 </span></span>= G * <span><span><span>ML</span><span>ms / </span></span><span>x^2
MT / (R-x)^2 = ML / x^2
So,
x = R * sqrt(ML * MT) - ML / (MT - ML)
R = is the distance between Earth and Moon.
</span></span></span>The result should be,
x = 3.83 * 10^7m
from the center of the Moon, and
R - x = 3.46*10^8 m
from the center of the Earth.
(2) As the distance from the center of the Earth is the number we found before,
d = R - x = 3.46*10^8m
The acceleration at this point is
g = G * MT / d^2
g = 3.33*10^-3 m/s^2
consider the motion of the tennis ball in downward direction
Y = vertical displacement = 400 m
a = acceleration = acceleration due to gravity = 9.8 m/s²
v₀ = initial velocity of the ball at the top of building = 10 m/s
v = final velocity of the ball when it hits the ground = ?
using the kinematics equation
v² = v²₀ + 2 a Y
inserting the values
v² = 10² + 2 (9.8) (400)
v = 89.11 m/s
decreased 5 times
Explanation: if the force increases 5 times between them would decrease 5 times