Archimedes found a piece of gold and a piece of silver with exactly the same mass. He dropped the gold into a bowl filled to the brim with water and measured the volume of water that spilled out. Then he did the same thing with the piece of solver. Although both metals had the same mass, the silver gad a larger volume; therefore, it displaced more water than the gold did. That's because the silver was less dense than gold. Afterwards he applied the same method to the crown for the king he served who had got a new crown from a jeweler who gave it to him. Archimedes found a piece of pure gold that had the same mass as the crown. He placed the pure gold chuck and the crown in water, one at a time. The crown displaced more water the piece of gold. Therefore, its density was less than pure gold.
(d) Acceleration is a vector quantity
Answer:
a) 
b) 
c) 
d) 
Explanation:
Given:
- mass of the astronaut,
- vertical displacement of the astronaut,
- acceleration of the astronaut while the lift,
a)
<u>Now the force of lift by the helicopter:</u>
Here the lift force is the resultant of the force of gravity being overcome by the force of helicopter.
where:
force by the helicopter
force of gravity
b)
The gravitational force on the astronaut:
d)
Since the astronaut has been picked from an ocean we assume her initial velocity to be zero, 
using equation of motion:
c)
Hence the kinetic energy:
According to the Law of Inertia, our upper body was in rest and it wanted to remain in that condition.....
