Question

A body is thrown at angle ${30}^o$ to the horizontal with the velocity of 30 m/s. After 1 sec, its velocity will be (inm/s) $(g-=10{m/s}^2)$

• A. $10\sqrt{7}$
• B. $700\sqrt{10}$
• C. $100\sqrt{7}$
• D. $\sqrt{40}$

Answer 1

The correct option is A $10\sqrt{7}$

Given,

$u=30m/s$

$\theta ={30}^0$

$t=1s$

$g=10m/s^2$

Horizontal component of velocity along x-axis after $1s$ is

$v_x=u_x+gt$

$v_x=ucos\theta +0\times 1$

$v_x=30cos{30}^0$

$v_x=25.98m/s$

Vertical component of the velocity along y-axis after $1s$ is

$v_y=u_y-gt$

$v_y=30sin{30}^0-10\times 1$

$v_y=15-10$

$v_y=5m/s$

Velocity of a body after $1s$ is

$\overrightarrow{v}=v_x\hat{i}+v_y\hat{j}$

$\overrightarrow{v}=25.98\hat{i}+5\hat{j}$

Magnitude, $v=|\overrightarrow{v}|=\sqrt{(25.98{)}^2+(5{)}^2}$

$v=\sqrt{700}$

$v=10\sqrt{7}m/s$

The correct option is A.