Motion in a Plane - ProjectileContact Number: 9667591930 / 8527521718

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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. ${\mathrm{tan}}^{-1}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)$

2. ${\mathrm{tan}}^{-1}\left(\mathrm{b}\right)$

3. ${\mathrm{tan}}^{-1}\left(\frac{\mathrm{b}}{\mathrm{a}}\right)$

4. ${\mathrm{tan}}^{-1}\left(\mathrm{a}\right)$

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) ${\mathrm{tan}}^{2}\theta $

(2) ${\mathrm{cot}}^{2}\mathrm{\theta}$

(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/s^{2})

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. ${\mathrm{R}}^{2}$

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