Answer:
The horizontal distance covered by the firework will be
Explanation:
Let acceleration due to gravity on the planet be g, initial velocity of the firework be u and angle made with the horizontal be ∅.
writing equation of motion in vertical direction:
and
therefore
writing equation of motion in horizontal direction:
therefore the equation becomes
therefore horizontal distance traveled =
Before we solve this, we should know this fact:
According to Newton's Law of Gravitation, the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The force acts along the line joining the centres of the two objects. It can be shown by this:
Now, let us check all the options.
A. As we move to higher altitudes, the force of gravity on us decreases.
<em>This </em><em>statement </em><em>is </em><em>true.</em>
The force of gravity is inversely proportional to the square of distance from the centre of the earth. If, we go up the surface of the earth, the distance from the centre of the earth increases and hence the value of force of gravity decrease. So, force of gravity decreases with altitude.
B. As we move to higher altitudes, the force of gravity on us increases.
<em>This </em><em>statement</em><em> </em><em>is </em><em>false.</em>
We have already got the result in option A. that the force of gravity decreases with altitude. It never increases with altitude.
C. As we gain mass, the force of gravity on us decreases.
<em>This </em><em>statement</em><em> </em><em>is </em><em>false.</em>
The force of gravity is directly proportional to the product of the masses. So, if increase our mass, then the force of gravity will also increase and if we decrease our mass, then the force of gravity decreases.
D. As we gain mass, the force of gravity on us increases.
<em>This </em><em>statement</em><em> is</em><em> </em><em>true.</em>
As mentioned earlier in option C., the force of gravity is directly proportional to the product of the masses of the earth and another object. So, as we gain mass, the force of gravity on us increases.
E. As we move faster, the force of gravity on us increases.
<em>This </em><em>statement</em><em> is</em><em> </em><em>true</em><em>.</em>
Here, we have to consider a different formula. According to Newton's Second Law,
F = ma, where F is the force, m is the mass and a is the acceleration.
In other words,
F ∝ a, i.e., force is directly proportional to acceleration.
We know, acceleration is the rate of change of velocity of an body within a time period.
So, if speed is increased, then acceleration will also be greater, which results in the increase of force. So, as we move faster, the force of gravity on us increases.
<u>Answers:</u>
A: As we move to higher altitudes, the force of gravity on us decreases.
D: As we gain mass, the force of gravity on us increases.
E: As we move faster, the force of gravity on us increases.
Hope you could understand.
If you have any query, feel free to ask.