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A projectile starts with speed u at an angle $\mathrm{\theta }$ from the horizontal ground. The average velocity of the projectile between the point of projection and the point of arrival on the ground is:
(1) usin$\mathrm{\theta }$
(2) 2usin$\mathrm{\theta }$
(3) ucos$\mathrm{\theta }$
(4) 2ucos$\mathrm{\theta }$

The trajectory of a projectile in the vertical plane is y = ax - ${\mathrm{bx}}^2$ where a and b are constants, x and y are horizontal and vertical displacements from point of projection. The angle of projection from the horizontal is
1.  ${\tan }^{-1} \left(\frac{\mathrm{a}}{\mathrm{b}}\right)$
2.  ${\tan }^{-1} \left(\mathrm{b}\right)$
3.  ${\tan }^{-1} \left(\frac{\mathrm{b}}{\mathrm{a}}\right)$
4.  ${\tan }^{-1} \left(\mathrm{a}\right)$

A particle is thrown horizontally from a pole of height 500 m with an initial speed of 50 m/s. The distance between the foot of the pole and striking point of the particle on the ground is: (g = 10 m/${\mathrm{s}}^2$)
(1) 100 m
(2) 250 m
(3) 500 m
(4) 1000 m

Two balls are projected to acquire same range with the same initial speed u but at different angles of projection. If maximum height acquired by balls are ${\mathrm{H}}_1 \mathrm{and} {\mathrm{H}}_2$, then (${\mathrm{H}}_1 + {\mathrm{H}}_2$) is: (angle of projection of one projectile is $\mathrm{\theta }$)
(1) ${\tan }^2 \theta$
(2) ${\cot }^2 \mathrm{\theta }$
(3) $\frac{{\mathrm{u}}^2}{2\mathrm{g}}$
(4) tan $\mathrm{\theta }$

A particle of mass 6 kg moves with an initial velocity of $\overrightarrow{\mathrm{v}} = \left(8\hat{\mathrm{i}} + 8\hat{\mathrm{j}}\right)$ m/s. A constant force of $\overrightarrow{\mathrm{F}}=-30\hat{\mathrm{j}}$ N is applied to the particle. Initially, the particle was at (0, 0). The x-coordinate of the particle, when its y-coordinate again becomes zero is given by
(1) 6.0 m 
(2) 12.8 m
(3) 8 m
(4) 25.6 m

A projectile is projected with speed u at an angle of 30° with the vertical from the ground. The angle between the acceleration of the projectile and its velocity at the time of striking the horizontal ground is:
(1) 30°
(2) 60°
(3) 45°
(4) 0°

A missile is fired for maximum range with an initial velocity of 20 m/s, then the maximum height of missile is: (Take \(g=10\) m/s²)
1. 20 m
2. 30 m
3. 10 m
4. 40 m

Two projectiles projected with the same speed at angles $\mathrm{\theta }$ and (90° - $\mathrm{\theta }$) from the same point, then ${\mathrm{H}}_1 \times {\mathrm{H}}_2$ is equal to: (where symbols have their usual meanings)
1.  $\frac{{\mathrm{R}}^2}{16}$
2.  $\frac{{\mathrm{R}}^2}{8}$
3.  $\frac{{\mathrm{R}}^2}{4}$
4.  ${\mathrm{R}}^2$