In projectile motion if air resistance (or any of such force opposing motion) is taken into consideration, then
1. Projectile would deviate from its idealised parabolic trajectory.
2. Range would be less than that in absence of air.
3. Maximum height attained would be greater than that in absence of air.
4. Both (1) and (2) are correct.
View Answer
Air resistance acts opposite to the direction of motion, decreasing velocity. This causes deviation from the ideal symmetric parabolic trajectory and decreases both the range and maximum height. Thus, (1) and (2) are correct.
A swimmer wants to cross the river in shortest possible time, The angle \(theta\) made by the swimmer with flow of river is
1. \(\theta = 0^\circ\)
2. \(\theta > \frac{\pi}{2}\)
3. \(\theta = \frac{\pi}{2}\)
4. \(0 < \theta < \frac{\pi}{2}\)
View Answer
The time to cross a river is \(t = \frac{d}{v \sin \theta}\), where \(theta\) is the angle with the river flow. For \(t\) to be minimum, \(sin \theta\) must be maximum, which occurs at \(\theta = 90^\circ = \frac{\pi}{2}\).
Assertion (A): Path of a projected ball is parabolic in uniform gravitational field for oblique projection in absence of air resistance.
Reason (R): Gravitational force is always act perpendicular to velocity during the motion of a projectile.
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
View Answer
The path of a projectile is a parabola under constant gravitational acceleration. Gravitational force acts vertically downwards, which is perpendicular to the velocity only at the highest point of its trajectory, so R is false.
Assertion (A): In any interval, the magnitude of displacement is always less than or equal to the distance travelled.
Reason (R): For a particle travelling in a straight line with constant acceleration, the magnitude of the change in the velocity during any interval is always less than or equal to the change in the speed during that interval.
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
View Answer
Displacement is the straight-line distance, so its magnitude is always \(le\) distance. When a particle reverses its direction of motion, the magnitude of change in velocity can be greater than the change in speed, so R is false.
Assertion (A): A particle with constant acceleration always moves along a straight line.
Reason (R): A particle with constant acceleration will not change direction of motion.
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
View Answer
A projectile experiences constant acceleration (g) but follows a parabolic path. Also, a ball thrown vertically upwards under gravity has constant acceleration but reverses its direction of motion, making both statements false.