Answer:
The answer is below
Explanation:
Newton's law of gravity states that the force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The law is expressed by the formula:

The masses and distances for this question is in common units, Therefore the result would be in ratios
a) 4 MEarth / 2 MSolar / 3 AU
The force (F) = (4 * 3) / 3² = 4/3
b) 1 MEarth / 1 MSolar / 1 AU
The force (F) = (1 * 1) / 1² = 1
c) 1 MEarth / 2 MSolar / 2 AU
The force (F) = (1 * 2) / 2² = 1/2
Given
v = 343 m/s
ac = 5g
ac = 5*9.8 m/s^2
ac = 49 m/s^2
where,
v: velocity
ac = centripetal aceleration
Procedure
We call the acceleration of an object moving in uniform circular motion—resulting from a net external force—the centripetal acceleration ac; centripetal means “toward the center” or “center seeking”.
Formula

The minimum radius not to exceed the centripetal acceleration is 2401 m.
The first thing to do is to define the origin of the coordinate system as the point at which the moped journey begins.
Then, you must write the position vector:
r = -3j + 4i + 3j
Rewriting
r = 4i
To go back to where you started, you must go
d = -4i
That is to say, must travel a distance of 4Km to the west.
Answer
West, 4km.
Answer:
Part a)

Part b)

Part c)

Part d)

Part e)

Part f)

Part g)

Explanation:
Initial speed of the launch is given as
initial speed = 
angle =
degree
Now the two components of the velocity

similarly we have

Part a)
Now we know that horizontal range is given as

maximum height is given as

so we have

time of flight is given as



Part b)
Now the speed of the ball in x direction is always constant
so at the peak of its path the speed of the ball is given as



Part c)
Initial vertical velocity is given as


Part d)
Initial speed is given as

so we will have


Part e)
Angle of projection is given as



Part f)
If we throw at same speed so that it reach maximum height
then the height will be given as


Part g)
For maximum range the angle should be 45 degree
so maximum range is

