Answer:
s = 1.7 m
Explanation:
from the question we are given the following:
Mass of package (m) = 5 kg
mass of the asteriod (M) = 7.6 x 10^{20} kg
radius = 8 x 10^5 m
velocity of package (v) = 170 m/s
spring constant (k) = 2.8 N/m
compression (s) = ?
Assuming that no non conservative force is acting on the system here, the initial and final energies of the system will be the same. Therefore
• Ei = Ef
• Ei = energy in the spring + gravitational potential energy of the system
• Ei = \frac{1}{2}ks^{2} + \frac{GMm}{r}
• Ef = kinetic energy of the object
• Ef = \frac{1}{2}mv^{2}
• \frac{1}{2}ks^{2} + (-\frac{GMm}{r}) = \frac{1}{2}mv^{2}
• s =
s =
s = 1.7 m
The density of the fluid is 776.3 
<u>Explanation:</u>
Buoyant force is the upward pushing force whenever an object is trying to get immersed in fluid. So this is the force given by the fluid on the object which is trying to get immersed. The buoyant force is found to be directly proportional to the product of density of the object, volume of the object. And here the acceleration due to gravity will be acting as proportionality constant.

As, buoyant force is given as 671 N and volume is 0.0882
and acceleration is known as 9.8 m/
. Then density is

Thus,

Density is 776.3 kg
.
Answer:
They both rises to same height.
Explanation:
When an object is sliding up in friction less surface than according to conservation of energy its potential energy will be converted into kinetic energy.

Here, m is the mass, v is the velocity, g is the acceleration due to gravity and H is the height.
Here the height is independent on the mass of an object and its only depend on velocity.
Now according to the question, two objects have same velocity but they have different masses.
Therefore, they rises to the same height because height will not change with mass.
The kinetic energy decreases