Answer:
See description
Explanation:
Frist we need to know the longitude of tape which is unwinding. Such relationship can be obtained with arc length. An arc length is the distance bewteen two points in a curve.
The relationship is:
Where is the arc length or distance, theta is the angle that results from the initial point of the measure to the final point, and r is the radius of a circumference.
Now let be length the unwinded tape. Change by and you ge the relationship:
if you unwind the tape by one revolution () you get the perimeter of a cricle , if you unwind it two times then and so on.
Then we have that the derivative of is
so we replace:
the derivative of theta with respect to t is ω(t) by definition:
The result is the relationship between angular velocity and the velocity and tangential velocity at the point r
The mass of the astronaut is still 65 kilograms. Mass is constant or doesn't change no matter where you are.
Explanation:
a) The height of the ball h with respect to the reference line is
so its initial gravitational potential energy is
b) To find the speed of the ball at the reference point, let's use the conservation law of energy:
We know that the initial kinetic energy as well as its final gravitational potential energy are zero so we can write the conservation law as
Note that the mass gets cancelled out and then we solve for the velocity v as