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Newton's law of universal gravation states that every particle attracts every other particles in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers
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Solving for the acceleration of the bullet
acceleration = (vf^2 – vi^2) / 2d
acceleration = ((280 m/s)^2 – (420 m/s)^2) / (2 * 0.12 m)
acceleration = (78400 - 176400) / 0.24 m
acceleration = -98000 / 0.24
acceleration = -408333 m/s^2
Solving for contact time with board
t^2 = 2d/a
t^2 = 2 * 0.12 m / 408333 m/s^2
t^2 = 0.24 m / 408333 m/s^2
t^2 = 5.8775558 x 10^-7
t = 0.0007666 s or 767 microseconds
(I was only able to do A and B)
First, let's calculate the total mechanical energy when the block is at rest and the spring is compressed 5 cm:
Now, let's use this total energy to calculate the velocity when the spring is compressed by 2.5 cm:
Therefore the speed is 1.026 m/s.
A second important difference between comets coming from the Kuiper Belt and from the Oort cloud is represented by their different characteristic periods.
In fact, short period comets are thought to generate in the Kuiper belt and have rather predictable orbits with short periods (up to 200 years). There are two major families of short period comets: the Jupiter family with periods of less than 20 years and the Halley family with periods form 20 to 200 years. That's short
