A particle is projected with initial speed of V0 and angle of θ. Find the horizontal displacemen

step 1 As we know, in any projectile motion, the horizontal component of speed remain constant. So we w

A particle is projected with initial speed of V0 and angle...

A particle is projected with initial speed of $\mathrm{V}_{0}$ and angle of $\theta$. Find the horizontal displacement when its velocity is perpendicular to initial velocity. (A) $\left[\left(\mathrm{V}_{0}^{2}\right) /(\operatorname{gtan} \theta)\right]$ (B) $\left[\left(\mathrm{V}_{0}^{2}\right) /(\mathrm{g} \sin \theta)\right]$ (C) $\left[\left(\mathrm{V}_{0} \sin \theta\right) / \mathrm{g}\right]$ (D) $\left[\left(\mathrm{V}_{0}^{2}\right) /(\tan \theta)\right]$

A particle is projected with initial speed of $\mathrm{V}_{0}$ and angle of $\theta$. Find the horizontal displacement when its velocity is perpendicular to initial velocity.
(A) $\left[\left(\mathrm{V}_{0}^{2}\right) /(\operatorname{gtan} \theta)\right]$
(B) $\left[\left(\mathrm{V}_{0}^{2}\right) /(\mathrm{g} \sin \theta)\right]$
(C) $\left[\left(\mathrm{V}_{0} \sin \theta\right) / \mathrm{g}\right]$
(D) $\left[\left(\mathrm{V}_{0}^{2}\right) /(\tan \theta)\right]$

Key Concepts

Trigonometric Relationships

This concept involves the use of sine, cosine, and tangent functions to relate the angles and sides of triangles formed by vector components. These relationships are essential in determining the magnitudes of horizontal and vertical parts of velocity, as well as in setting up equations that describe the conditions of the motion.

Dot Product and Orthogonality

This concept refers to the mathematical approach used to determine if two vectors are perpendicular. By taking the dot product of the velocity vector at any instant with the initial velocity vector and setting it to zero, one can derive conditions needed to ascertain when the direction of motion becomes perpendicular to the launch direction.

Kinematic Equations

These are the equations that describe the motion of objects in terms of displacement, velocity, acceleration, and time. In projectile motion, they are used to determine the position and velocity of the object at any given time, which is crucial when solving for specific conditions, such as perpendicularity between velocity vectors.

Projectile Motion

This concept deals with objects moving under the influence of gravity after an initial launch. It involves splitting the motion into horizontal and vertical components, where the horizontal motion exhibits constant velocity while the vertical motion features constant acceleration due to gravity.

Component Analysis of Vectors

This key concept involves breaking down an initial velocity vector into its horizontal and vertical parts using trigonometric functions. This separation is critical in analyzing different aspects of motion, allowing distinct treatment of the independent horizontal motion and the accelerated vertical motion in projectile problems.

Please give Ace some feedback