Question

In the given figure velocity and acceleration in vector form are :-

• A. $\frac{4v}{5}\hat{i}+\frac{3v}{5}\hat{j}$
• B. $\frac{4v}{5}\hat{i}-\frac{3v}{5}\hat{j}$
• C. $g\hat{j}$
• D. $-g\hat{j}$

Answer 1

Answer: (A)

$\frac{4v}{5}\hat{i}+\frac{3v}{5}\hat{j}$

Answer 2

The initial velocity vector $\vec{v}$ has a magnitude $v$ and is directed at an angle of $37^\circ$ with the horizontal. The horizontal component of the velocity is $v_x = v \cos(37^\circ)$ and the vertical component is $v_y = v \sin(37^\circ)$. Using the standard approximations $\cos(37^\circ) \approx \frac{4}{5}$ and $\sin(37^\circ) \approx \frac{3}{5}$, we have $v_x = v \times \frac{4}{5} = \frac{4v}{5}$ and $v_y = v \times \frac{3}{5} = \frac{3v}{5}$. Since the velocity is in the first quadrant (positive x and positive y directions), the initial velocity vector is $\vec{v} = v_x \hat{i} + v_y \hat{j} = \frac{4v}{5}\hat{i} + \frac{3v}{5}\hat{j}$.