$A$ projectile is thrown in the upward direction making an angle of $60^{\circ}$ with the horizontal with a velocity of $140 \,ms^{-1}$. Then the time after which its velocity makes an angle $45^{\circ}$ with the horizontal is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,s$)

$A$ ball is dropped from a height of $49\,m$. The wind is blowing horizontally. Due to wind,a constant horizontal acceleration is provided to the ball. Choose the correct statement$(s)$. (Take $g = 9.8\,m/s^2$)

$A$ particle is moving with velocity $\vec v = K(y\hat i + x\hat j)$ where $K$ is a constant. The general equation for its path is

$A$ body is revolving with a constant speed along a circle. If its direction of motion is reversed but the speed remains the same,then which of the following statements is true?

An aeroplane executes a horizontal loop at a speed of $720 \text{ km/h}$ with its wings banked at $45^{\circ}$. What is the radius of the loop (in $\text{ km}$)? Take $g = 10 \text{ m/s}^2$.

Fill in the blanks:
$(a)$ If $\overrightarrow A \cdot \overrightarrow B = AB$,then the angle between $\overrightarrow A$ and $\overrightarrow B$ is ............
$(b)$ The velocity of a projectile at its maximum height is ............ (Take the angle of projection as $\theta$).
$(c)$ The projection of $\widehat i - 2\widehat j + 4\widehat k$ on the $y$-axis is ............