Answer:
Approximate linear dimension is 2 light years.
Explanation:
Radius of the spiral galaxy r = 62000 LY
Thickness of the galaxy h = 700 LY
Volume of the galaxy = πr²h
= (3.14)(62000)²(700)
= (3.14)(62)²(7)(10)⁸
= 84568×10⁸
=
(LY)³
Since galaxy contains number of stars = 1078 billion stars ≈ 
Now volume covered by each star of the galaxy = 
= 
= 7.839 Light Years
Now the linear dimension across the volume
= 
= 
= 1.99 LY
≈ 2 Light Years
Therefore, approximate linear dimension is 2 light years.
F=ma
8480=26.5m
m=8480/26.5
m=320
The mass of the cart is 320kg.
The force is -12,000 N
Explanation:
First of all, we calculate the acceleration of the ball, by using the following suvat equation:

where:
v = 0 is the final velocity of the baseball (it comes to rest)
u = 40 m/s is the initial velocity
a is the acceleration
s = 2.0 cm = 0.02 m is the displacement of the ball
Solving for a,

Now we can calculate the average force exerted on the ball, by using Newton's second law:

where
m = 300 g = 0.3 kg is the mass of the ball
is the acceleration
Substituting,

where the negative sign indicates that the direction of the force is opposite to the direction of motion of the ball.
Learn more about forces:
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Answer:
96.21 ft/s
Explanation:
To solve this, you only need to use one expression which is:
Vf² = Vo² + 2gh
g = 9.8 m/s²
However, this exercise is talking in feet, so convert the gravity to feet first:
g = 9.8 * 3.28 = 32.15 ft/s²
Vo is zero, because it's a free fall and in free fall the innitial speed is always zero. With this, let's calculate the speed at 2 seconds, with a height of 64 ft, and then with the 256 ft:
V1 = √2*32.15*64
V1 = 64.15 ft/s
V2 = √2*32.15*256
V2 = 128.3 ft/s
So the average rate is:
V = 128.3 + 64.15 / 2
V = 96.22 ft/s