It would be helpful if you draw the figure of the problem. You will see that a right triangle would be constructed by the problem where 19.0 is the angle between the hypotenuse and the base of the triangle. It is said that the force acting is said to be 9.0 N at the said angle to the horizontal. Using trigonometric relations,
cos 19 = adjacent / hypotenuse = horizontal component / 9
horizontal component = 8.51 N
Explanation:
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The magnitude of the force is 18.6 N
Explanation:
The work done by a force on an object is given by

where
F is the magnitude of the force
d is the displacement of the object
is the angle between the direction of the force and of the displacement
For the block in this problem, we have
is the work done
d = 1.35 m is the displacement of the block
is the angle between the force and the displacement
Solving for F, we find the magnitude of the force:

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<span>b) The force with a distance of 150 km is 889 N
c) The force with a distance of 50 km is 8000 N
This question looks like a mixture of a question and a critique of a previous answer. I'll attempt to address the original question.
Since the radius of the spherical objects isn't mentioned anywhere, I will assume that the distance from the center of each spherical object is what's being given. The gravitational force between two masses is given as
F = (G M1 M2)/r^2
where
F = Force
G = gravitational constant
M1 = Mass 1
M2 = Mass 2
r = distance between center of masses for the two masses.
So with a r value of 100 km, we have a force of 2000 Newtons. If we change the distance to 150 km, that increases the distance by a factor of 1.5 and since the force varies with the inverse square, we get the original force divided by 2.25. And 2000 / 2.25 = 888.88888.... when rounded to 3 digits gives us 889.
Looking at what looks like an answer of 890 in the question is explainable as someone rounding incorrectly to 2 significant digits.
If the distance is changed to 50 km from the original 100 km, then you have half the distance (50/100 = 0.5) and the squaring will give you a new divisor of 0.25, and 2000 / 0.25 = 8000. So the force increases to 8000 Newtons.</span>