
Two projectiles of the same mass have their maximum kinetic energies in ratio and the ratio of their maximum heights is also . Then what is the ratio of their ranges?
(A)
(B)
(C)
(D)
Answer
139.8k+ views
Hint We are given here with the kinetic energy ratio and the ratio of maximum height and we are asked to find out the ratio of their ranges. So we will find the ratio of their velocities and angles of the projectile and use the formula for range.
Formula used
Where, is the kinetic energy of the projectile, is the mass of the projectile and is the initial velocity of the projectile.
Where, is the maximum height of the projectile, is the initial velocity of the projectile, is the angle of the projectile with the horizontal and is the acceleration due to gravity.
Where, is the range of the projectile, is the initial velocity of the projectile, is the angle of the projectile with the horizontal and is the acceleration due to gravity.
Complete Step By Step Solution
We are given,
Thus, putting in the formula for kinetic energy, we can say
Thus, after cancellation, we get
Thus, we get
Now,
After cancellation and Putting in , we get
Thus, we can say
Now,
After cancellation and putting in and , we get
Hence, the correct option is (B).
Note We evaluated the value of and . This was for being more precise with the answer. Moreover, the value of could . But the value of velocity of a projectile cannot be negative. Thus, we took the value of to be .
Formula used
Where,
Where,
Where,
Complete Step By Step Solution
We are given,
Thus, putting in the formula for kinetic energy, we can say
Thus, after cancellation, we get
Thus, we get
Now,
After cancellation and Putting in
Thus, we can say
Now,
After cancellation and putting in
Hence, the correct option is (B).
Note We evaluated the value of
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