Hi there!
Recall the conservation of momentum:

For this type of inelastic collision:

Thus, the initial momentum equal the final momentum if there are no external forces.
We can begin by writing out this problem:


Explanation:
hopefully that makes sense. the position doesn't change over the 5 seconds, meaning it's stopped but time still continues. then when the slope is negative this shows the bear's position becoming negative (backing up, changing direction).
<h2>
Answer: 469 feet</h2>
Explanation:
This problem is a good example of Vertical motion, where the main equation for this situation is:
(1)
Where:
is the height of the stone at 6s (the value we want to find)
is the initial height of the stone
is the initial velocity of the stone
is the time at which we need to find the height
is the acceleration due to gravity
Having this clear, let's find
from (1):
(2)
Finally:
This is the height of the stone at t=6s
We apply the gravity calculation expressed in the formula: g=GM/r2
where G is the gravitational constant, m is the mass and r is the radius
r=√GM/g
(1) Radius = √6.674e-11*5.972e24/8 = 7058 kms Earth radius or surface of earth from center of earth= 6400 kmsSo r= 658 kms from surface of earth.
Gravity 8m/s2 will be at 658 kms from surface of earth.
(2) half gravity= 9.8/2= 4.9 m/s2 Radius=√6.674e-11*5.972e24/4.9 = 9019 kms Half Gravity will exist at 9019-6400= 2619 kms from surface of earth.