Question

In a projectile motion from a point of horizontal surface to another point on the same surface (Take $\overrightarrow{a}=$ acceleration and $\overrightarrow{v}=$ instantaneous velocity)

• A. $\overrightarrow{a}\cdot \overrightarrow{v}=0$ at maximum height
• B. $\overrightarrow{a}\cdot \overrightarrow{v}=0$ only if angle of projection is ${90}^{\circ }$
• C. $\overrightarrow{a}\times \overrightarrow{v}=$ constant every where in air
• D. None of these

Answer 1

Answer: (A), (C)

The correct options are
A $\overrightarrow{a}\cdot \overrightarrow{v}=0$ at maximum height
C $\overrightarrow{a}\times \overrightarrow{v}=$ constant every where in air

At highest point
$\overrightarrow{a}=-g\hat{j}$
$\overrightarrow{v}=u\cos \theta \hat{i}\Rightarrow \overrightarrow{a}\cdot \overrightarrow{v}=0$

Option A is correct.

$\overrightarrow{v}=u\cos \theta \hat{i}+u\sin \theta \hat{j}-gt\hat{j}$
$\overrightarrow{a}=-g\hat{j}$
$\overrightarrow{a}\times \overrightarrow{v}=u\cos \theta g\hat{k}=constant$

Option C is correct.