Projectile Motion – Time of Flight and Range Scaling – Rankers Physics
Topic: Kinematics
Subtopic: Ground to Ground Projectile

Projectile Motion – Time of Flight and Range Scaling

Assertion (A): When speed of projection of a body is made (n) times, its time of flight becomes (n) times.
Reason (R): At this speed, the range of projectile becomes (n^2) times.
 
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution:

Assertion (A): Time of flight \(T = \frac{2u sin\theta}{g}\). If (u) is replaced by (nu), (T' = nT). So (A) is True.

Reason (R): Horizontal range \(R = \frac{u^2 sin(2\theta)}{g}\). If (u) is replaced by (nu), (R' = n^2 R). So (R) is True.

Both statements are true. However, the scaling of range (R) does not explain the scaling of time of flight (A). They are independent consequences of initial speed scaling. So (R) is not the correct explanation for (A). Option (2) is correct.

Leave a Reply

Your email address will not be published. Required fields are marked *