Answer:
You just double the number of boxes it goes higher. Then triple the number for the second question. But don't change the time.
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A. The closet point in the Moon's orbit to Earth . . . . . perigee
B. The farthest point in the Moon's orbit to Earth . . . . . apogee
C. The Sun's orbit that is closest to the Moon . . . . . a meaningless description
D. The closest point in Earth's orbit of the Sun . . . . . perihelion
-- The farthest point in Earth's orbit of the Sun . . . . . aphelion
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<span>14.79 m/s
At the top of the loop, there's 2 opposing forces. The centripetal force that's attempting to push the roller coaster away and the gravitational attraction. These 2 forces are in opposite directions and their sum is 0.80 mg where m = mass and g = gravitational attraction. So let's calculate the amount of centripetal force we need.
0.80 = F - 1.00
1.80 = F
So we need to have a centripetal force that's 1.8 times the local gravitational attraction which is 9.8 m/s^2. So
1.8 * 9.8 m/s^2 = 17.64 m/s^2
The formula for centripetal force is
F = mv^2/r
where
F = force
m = mass
v = velocity
r = radius
We can eliminate mass from the equation since the same mass is being affected by both the centripetal force and gravity. So:
F = v^2/r
17.64 m/s^2 = v^2/12.4 m
218.736 m^2/s^2 = v^2
14.78972616 m/s = v
So the velocity at the top of the loop (rounded to 2 decimal places) is 14.79 m/s.</span>
