Motion in plane practice · Easy

The angle $\theta$ between the vector $\mathbf{p}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and unit vector along $X$-axis is

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water (in km/hr) is

Assertion: Three projectiles are moving in different paths in the air. Vertical component of relative velocity between any of the pair does not change with time as long as they are in air. (Neglecting the effect of air friction)
Reason: Relative acceleration between any of the pair of projection is zero.

Assertion: If $|\vec{A}+\vec{B}|=| \vec{A}-\vec{B} \mid$, then the angle between $\vec{A}$ and $\vec{B}$ is $90^{\circ}$.
Reason: $\vec{A}+\vec{B}=\vec{B}+\vec{A}$

What is the range of a projectile thrown with velocity $98 \mathrm{~ms}^{-1}$ with angle $30^{\circ}$ from horizontal ?

At the top of the trajectory of a projectile, the acceleration is

Consider a vector $\mathbf{F}=4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}$. Another vector perpendicular to $\mathbf{F}$ is

If $\mathbf{A} \times \mathbf{B}=\mathbf{B} \times \mathbf{A}$, then the angle between $\mathbf{A}$ and $\mathbf{B}$ is

$\mathrm{~A}$ body is projected at an angle of $30^{\circ}$ with the horizontal with momentum $p$. At its highest point, the magnitude of the momentum is

A vector is added to an equal and opposite vector of similar nature, forms a