Ground to Ground Projectile: Practice Problem & Solution
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.
Solution Explained:
To solve this problem, we apply the core principles of Ground to Ground Projectile. Understanding the underlying formula is key to arriving at the correct answer below:
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.
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