A particle of mass m is projected with velocity v moving at...

A particle of mass $m$ is projected with velocity $v$ moving at an angle of $45^{\circ}$ with horizontal. The magnitude of angular momentum of projectile about point of projection when particle is at maximum height, is : (a) zero (b) $\frac{m v^{3}}{4 \sqrt{2} g}$ (c) $\frac{m v^{3}}{\sqrt{2} g}$ (d) $m \sqrt{2} g h^{3}$

A particle of mass $m$ is projected with velocity $v$ moving at an angle of $45^{\circ}$ with horizontal. The magnitude of angular momentum of projectile about point of projection when particle is at maximum height, is :
(a) zero
(b) $\frac{m v^{3}}{4 \sqrt{2} g}$
(c) $\frac{m v^{3}}{\sqrt{2} g}$
(d) $m \sqrt{2} g h^{3}$

Key Concepts

Projectile Motion

This concept refers to the motion of an object that is projected into the air and then moves under the influence of gravity only. It involves breaking the initial velocity into horizontal and vertical components, determining the time of flight, the maximum height, and the horizontal displacement. Understanding projectile motion is crucial, as it allows one to analyze the position and velocity of a projectile at various points along its trajectory, such as at maximum height.

Angular Momentum

Angular momentum is a measure of the quantity of rotation of an object about a given point and is defined as the cross product of the position vector and the linear momentum of the object. It is particularly useful for analyzing rotational effects in mechanics. In the context of projectile motion, calculating angular momentum at a specific point, such as the maximum height, involves determining the position of the object relative to the point of projection and its instantaneous momentum.

Vector Cross Product

The vector cross product is an operation on two vectors in three-dimensional space that produces a third vector perpendicular to the plane containing the original vectors. The magnitude of this vector is given by the product of the magnitudes of the two original vectors and the sine of the angle between them. This concept is essential for calculating angular momentum, which is defined as the cross product of the position vector and the momentum vector.

Transcript

Please give Ace some feedback