A projectile is fired at an angle of 45º with the horizontal. Elevation angle of the projectile at its highest point, as seen from the point of projection, is :

1. 45º

2. 60º

3. ${\tan }^{-1}\frac{1}{2}$

4. ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is -

1. 15º

2. 30º

3. 45º

4. 60º

A particle moves in the x – y plane according to the rule x = a sin ωt and y = a cos ωt. 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°-θ) and (45°+θ), 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 ($\sqrt{3}$, 3). The path of the particle makes an angle of .......................with the x-axis :

1. 30^o

2. 45^o

3. 60^o

4. 0^o

A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on the level ground, the magnitude of change in its momentum will be:

1.  $2\mathrm{mv}$

2.  $\mathrm{mv}/\sqrt{2}$

3.  $\mathrm{mv}\sqrt{2}$

4.  zero

A particle has initial velocity $(3\hat{\mathrm{i}} + 4\hat{\mathrm{j}})$ and has acceleration $(0.4\hat{\mathrm{i}}+ 0.3\hat{\mathrm{j}})$. Its speed after 10 s is

1. 7 units

2. 7$\sqrt{2}$units

3. 8.5 units

4. 10 units

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 sec, its velocity becomes 40 m/s towards the north. The average acceleration of the body is:

1.  $7 \mathrm{m}/{\mathrm{s}}^2$

2.  $\sqrt{7} \mathrm{m}/{\mathrm{s}}^2$

3.  $5 \mathrm{m}/{\mathrm{s}}^2$

4.  $1 \mathrm{m}/{\mathrm{s}}^2$