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. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
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.
Assertion (A): When the range of a projectile is maximum, the time of flight is the largest.
Reason (R): Horizontal range is maximum when angle of projection is (90^circ).
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A): Maximum range occurs at (theta = 45^circ). The largest time of flight occurs at (theta = 90^circ). Since these angles are different, the assertion is false. So (A) is False.
Reason (R): Horizontal range is maximum at (theta = 45^circ) (when (sin(2theta)=1)). At (theta = 90^circ), the range is zero. So (R) is False.
Since both (A) and (R) are false, option (4) is correct.
Consider the following two statements and tick the correct answer.
Statement A: In projectile motion, horizontal component of velocity of particle remains constant while its acceleration changes continuously.
Statement B: In projectile motion, particle moves such that its velocity and acceleration both changes continuously.
1. Statement A is correct while statement B is incorrect
2. Statement A is incorrect while statement B is correct
3. Both statement A and statement B are correct
4. Both statement A and statement B are incorrect
View Answer
In projectile motion, acceleration is constant throughout (equal to acceleration due to gravity \(\vec{g}\)). Thus, both statements are incorrect because they claim acceleration changes.