A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle $\mathrm{\theta }$ with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory, which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in m/s²) is: [Given, g = 9.8 m/s²]

1. 3.5

2. 5.9

3. 16.3

4. 110.8

 

A particle is moving such that its position coordinates (x, y) are (2m, 3m) at time t = 0, (6m, 7m) at time t = 2s and (13m, 14m) at time t = 5s. Average velocity vector (v_av) from t = 0 to t = 5s is

1. $\frac{1}{5}$(13$\hat{i}$+14$\hat{j}$)

2. $\frac{7}{3}$($\hat{i}$+$\hat{j}$)

3. 2($\hat{i}$+$\hat{j}$)

4. $\frac{11}{5}$($\hat{i}$+$\hat{j}$)

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


1.  -2i+3j

2.  -2i-3j

3.   2i-3j

4.  2i+3j

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. $\theta ={\tan }^{-1}\left(4\right)$

3. $\theta ={\tan }^{-1}\left(2\right)$                                         

4. $\theta =45°$

A particle has an initial velocity ($2\hat{i}+3\hat{j}$) and an acceleration ($0.3\hat{i}+0.2\hat{j}$). The magnitude of velocity after $10$ s will be:
1. $9 \sqrt{2} ~\text{units}$
2. $5 \sqrt{2} ~\text{units}$
3. $5 ~\text{units}$
4. $9~\text{units}$

A body is moving with velocity 30 m/s towards east. After 10 s its velocity becomes 40 m/s towards 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) $1 \mathrm{m}/{\mathrm{s}}^2$

A missile is fired for maximum range with an initial velocity of 20 m/s. If g=10 $\mathrm{m}/{\mathrm{s}}^2$, the range of the missile is:

1. 50 m                                                          2. 60 m

3. 20 m                                                          4. 40 m

A projectile is fired at an angle of 45$°$ with the horizontal. The elevation angle $\alpha$ of the projectile at its highest point as seen from the point of projection is:

1. 60$°$                                           2. ${\tan }^{-1}\left(\frac{1}{2}\right)$

3. ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$                               4. $45°$

A particle has an initial velocity $\left(3\hat{i}+4\hat{j}\right)$ and has an acceleration $\left(0.4\hat{i}+0.3\hat{j}\right)$. Its speed after 10 s is: 
1. $7$ unit
2. $7\sqrt{2}$ unit
3. $8$ unit
4. $8\sqrt{2}$ unit

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

1. $60°$                                         

2. $15°$

3. $30°$                                         

4. $45°$