Question

Assertion: The trajectory of a projectile is quadratic in Y and linear in X.
Reason: Y-component of trajectory is independent of X-component.
A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C) Assertion is correct Reason is incorrect
D) Both Assertion and Reason are incorrect.

Answer 1

Hint: To deal with this question let us first discuss the projectile motion. Considering an object is launched or thrown from the surface of the earth at some angle, the object moves in a curved path with an acceleration acting towards the centre of the earth. Such a type of motion is known as a projectile motion.

Complete step by step answer:
Let us first have a look at the given Assertion. The Assertion is ‘the trajectory of a projectile is quadratic in Y and linear in X’. We know that the trajectory of a projectile motion in the Y-direction is given by,
$y = x\tan \theta - \dfrac{{g{x^2}}}{{2{u^2}{{\cos }^2}\theta }}$ ……….. (1)
From equation (1) it is clear that the nature of the trajectory of a projectile is linear in the y-direction and quadratic in the x-direction.

Now let us look at the Reason. The Reason is ‘Y-component of trajectory is independent of X-component.’ Also, from equation (1) we can say that the Y-component is not independent of the X-component of the projectile motion.
From the above discussion, it is clear that both the Assertion as well as the Reason are incorrect.

Hence, option D is the correct answer option.

Note: Some important terms related to the projectile motion are given below.
Projectile: The object performing the projectile motion is known as a projectile.
Trajectory: The path followed by a projectile while performing the projectile motion is known as the trajectory of that projectile.
Range: The horizontal distance between the take-off or launch point to the point at which the projectile lands on the surface is termed as the range.