The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:

1.	\(\theta = \tan^{-1}\left(\frac{1}{4}\right)\)	2.	\(\theta = \tan^{-1}(4)\)
3.	\(\theta = \tan^{-1}(2)\)	4.	\(\theta = 45^{\circ}\)

A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. The acceleration of the particle is:

A body is moving with a velocity of \(30~\text{m/s}\) towards the east. After \(10~\text s,\) its velocity becomes \(40~\text{m/s}\) towards the north. The average acceleration of the body is:
1. \( 7~\text{m/s}^2\)
2. \( \sqrt{7}~\text{m/s}^2\)
3. \(5~\text{m/s}^2\)
4. \(1~\text{m/s}^2\)

A particle starting from the origin \((0,0)\) moves in a straight line in the \((x,y)\) plane. Its coordinates at a later time are ($\sqrt{3}$, \(3).\) The path of the particle makes an angle of __________ with the \(x\)-axis:
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(0\)

A car turns at a constant speed on a circular track of radius \(100~\text m,\) taking \(62.8~\text s\) for every circular lap. The average velocity and average speed for each circular lap, respectively, is:

The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\text{m/s}.\) Its velocity (in m/s) at the point \(B\) is:
              

A particle moves in space such that:
\(x=2t^3+3t+4;~y=t^2+4t-1;~z=2\sin\pi t\)
where \(x,~y,~z\)  are measured in meters and \(t\) in seconds. The acceleration of the particle at \(t=3\) seconds will be:

A particle is moving such that its position coordinates \((x,y)\) are \(​ (2~\text m,  3~\text m)​\) at time \(t=0,\)   \(​ (6~\text m,  7~\text m)​\) at time \(t=2~\text s\)  and \(​ (13~\text m,  14~\text m)​\) at time \(t=5~\text s.\)  The average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5~\text s\) is:

A particle starts moving with constant acceleration with initial velocity (\(\hat{\mathrm{i}}+5\hat{\mathrm{j}}\)$\stackrel{}{\mathrm{}}$) m/s. After \(4\) seconds, its velocity becomes (\(3\hat{\mathrm{i}}-2\hat{\mathrm{j}}\)) m/s. The magnitude of its displacement in 4 seconds is:
1. \(5\) m
2. \(10\) m
3. \(15\) m
4. \(20\) m