Kinematics Question 458
Question: Assertion: The maximum horizontal range of projectile is proportional to square of velocity. Reason: The maximum horizontal range of projectile is equal to maximum height attained by projectile.
Options:
A) If both assertion and reason are true and the reason is the correct explanation of the assertion.
B) If both assertion and reason are true but reason is not the correct explanation of the assertion.
C) If assertion is true but reason is false.
D) If the assertion and reason both are false.
E) If assertion is false but reason is true.
Show Answer
Answer:
Correct Answer: C
Solution:
$ R=\frac{u^{2}\sin 2\theta }{g} $ $ {R _{\max }}=\frac{u^{2}}{g} $ when $ \theta =45{}^\circ $ $ {R _{\max }}\propto u^{2} $
Height $ H=\frac{u^{2}{{\sin }^{2}}\theta }{2g} $
therefore $ {H _{\max }}=\frac{u^{2}}{2g} $
when $ \theta =90{}^\circ $
It’s clear that $ {H _{\max }}=\frac{{R _{\max }}}{2} $
