The range of a projectile is same when its maximum heights are and . The relation between and .

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R = \sqrt{h_{1} h_{2}}

R = 5 \sqrt{h_{1} h_{2}}

None of these

answer is A.

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Detailed Solution

Concept: The maximum height of the projectile along the horizontal plane is given is given by

and the maximum height of the projectile along the vertical plane is given by

When an item is launched or thrust vertically upward, it develops motion on its own inertia, or the inclination to remain constant. The force of gravity has a significant impact on the motion. In other words, the gravitational force acting on the projectile is the only force acting on it. Inertia is the quality of an item that tends to stay in its state of rest or motion until and unless it is disturbed by an external force.
The projectile motion has two types along the

-axis and along the

-axis.
Newton's law of projectile motion also says that only force is required to produce acceleration but not the motion.
The projection of the projectile should be done at an angle of

from the horizontal to the vertical.
Therefore, for these angles:
Question Image

and

Now, multiplying both the heights

and

Simplify the above equation.
Question Image

………….(1)
Maximum range of the projectile is
Question Image

……………..(2)
From equation (1) and equation (2) ,

Hence, option 1 is correct.

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