Q: At what angle of projection is the horizontal range of a projectile maximum for a given initial velocity?

The formula for horizontal range is $R = \frac{u^2 \sin(2\theta)}{g}$. The range is maximum when $\sin(2\theta) = 1$, which implies $2\theta = 90^\circ$, so $\theta = 45^\circ$.

Question 1

Which of the following is a vector quantity?

Accepted Answer

Displacement has both magnitude and direction and follows the laws of vector addition, making it a vector quantity, whereas speed, work, and mass are scalar quantities.

Question 2

The angle between two vectors $\vec{A}$ and $\vec{B}$ is given by $	heta$. What is the scalar product (dot product) of these two vectors?

Accepted Answer

The scalar product of two vectors $\vec{A}$ and $\vec{B}$ is defined as $AB \cos	heta$, which yields a scalar value representing the product of the magnitude of one vector and the component of the other along it.

Question 3

What is the direction of the cross product of two vectors $\vec{A}$ and $\vec{B}$ lying in the plane of the paper?

Accepted Answer

According to the right-hand rule, the cross product vector $\vec{A} 	imes \vec{B}$ is perpendicular to the plane containing both vectors $\vec{A}$ and $\vec{B}$, which means it is directed normally outward or inward relative to the paper.

Question 4

At what angle of projection is the horizontal range of a projectile maximum for a given initial velocity?

Accepted Answer

The formula for horizontal range is $R = \frac{u^2 \sin(2	heta)}{g}$. The range is maximum when $\sin(2	heta) = 1$, which implies $2	heta = 90^\circ$, so $	heta = 45^\circ$.

Question 5

The path of a projectile thrown with an initial velocity in a vertical plane is a:

Accepted Answer

Due to constant horizontal velocity and uniform vertical acceleration due to gravity, the trajectory of a projectile is parabolic in shape.

Motion in a Plane