Answer:
the maximum angular speed (in radians per second) of a Blu-ray disc as it rotates is 57.6 m/s
Explanation:
Given information:
diameter of the disc, d = 11 cm, r = 5.5 cm = 0.055 m
angular speed ω = 10000 rev/min = (10000 rev/min)(2π rad/rev)(1/60 min/s)
= 1000π/3 rad/s
to calculate the maximum angular speed we can use the following formula
ω = v/r
v = ωr
= (1000π/3)(0.055)
= 57.6 m/s
In what may be one of the most remarkable coincidences in
all of physical science, the tangential component of circular
motion points along the tangent to the circle at every point.
The object on a circular path is moving in that exact direction
at the instant when it is located at that point in the circle. The
centripetal force ... pointing toward the center of the circle ...
is the force that bends the path of the object away from a straight
line, toward the next point on the circle. If the centripetal force
were to suddenly disappear, the object would continue moving
from that point in a straight line, along the tangent and away from
the circle.
When the ball starts its motion from the ground, its potential energy is zero, so all its mechanical energy is kinetic energy of the motion:

where m is the ball's mass and v its initial velocity, 20 m/s.
When the ball reaches its maximum height, h, its velocity is zero, so its mechanical energy is just gravitational potential energy:

for the law of conservation of energy, the initial mechanical energy must be equal to the final mechanical energy, so we have

From which we find the maximum height of the ball:

Therefore, the answer is
yes, the ball will reach the top of the tree.