A projectile is fired at an angle of \(45^\circ\) with the horizontal. The elevation angle \(\alpha\) of the projectile at its highest point, as seen from the point of projection is:
1. \(60^\circ\)
2. \(tan^{-1}\left ( \frac{1}{2} \right )\)
3. \(tan^{-1}\left ( \frac{\sqrt{3}}{2} \right )\)
4. \(45^\circ\)
The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is:
1. \(15^{\circ}\)
2. \(30^{\circ}\)
3. \(45^{\circ}\)
4. \(60^{\circ}\)
A particle moves in the \((x\text-y)\) plane according to the rule \(x = a \sin (\omega t)\) and \(y = a \cos (\omega t)\). The particle follows:
1. | a circular path. |
2. | a parabolic path. |
3. | a straight line path inclined equally to x and y-axes. |
4. | an elliptical path. |
A car turns at a constant speed on a circular track of radius \(100\) m, taking \(62.8\) s for every circular lap. The average velocity and average speed for each circular lap, respectively, is:
1. | \(0,~0\) | 2. | \(0,~10\) m/s |
3. | \(10\) m/s, \(10\) m/s | 4. | \(10\) m/s, \(0\) |
For a projectile projected at angles \((45^{\circ}-\theta)\) and \((45^{\circ}+\theta)\), the horizontal ranges described by the projectile are in the ratio of:
1. \(1:1\)
2. \(2:3\)
3. \(1:2\)
4. \(2:1\)
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 (, \(3).\) 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 particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on level ground, the magnitude of change in its momentum will be:
1.
2.
3.
4. zero
A missile is fired for a maximum range with an initial velocity of \(20\) m/s. If \(g=10\) m/s2, then the range of the missile will be:
1. | \(50\) m | 2. | \(60\) m |
3. | \(20\) m | 4. | \(40\) m |
A body is moving with a velocity of \(30\) m/s towards the east. After \(10\) s, its velocity becomes \(40\) 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. \(1~\text{m/s}^2\)