A block is attached to a spring

block-spring-stone

A 15 kg block is firmly attached to a very light horizontal spring (k = 550 N/m) and resting on a smooth horizontal table. Suddenly it is struck horizontally by a 3 kg stone travelling with a velocity of 8 m/s to the right, whereupon the stone rebounds at 2 m/s to the left. Find the maximum distance that the block will compress the spring after the collision.

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Human-Powered Helicopter

HPHA student builds a human-powered helicopter (HPH). It is a helicopter powered by one person carried on board and the power is generated by pedaling.
This human-powered helicopter has the following parameters: diameter of helicopter rotor blades is 15 meters and total mass is 100 kg. The air density 1.3 kg/m^3.

Can the HPH take off?

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A cannon ball.

cannonA cannon ball is fired vertically upward with an initial speed of Vo. At the highest point it explodes into two pieces of equal masses. One of the pieces hits the ground with a speed of 2Vo.
What is the speed of the second piece when it hits the ground?
How long was the second piece in the air?

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