2D Motion as Two 1D Motions

Q.

A body of mass m is thrown at an angle θ to the horizontal with the initial velocity u. Find the instantaneous power of gravity as function of time.

1. mg(gt - u cos)

2. mg(gt - u cot)

3. mg(gt - u sin)

4. mg(gt - u tan)

Q.

The rod is slipping. Velocity and acceleration of one end of rod are given. Find the angular speed and the acceleration of corner P.

1. 

2. 

3. 

4. 

Q.

In the diagram particle A moves along the line y = 25$\sqrt{3}$ m with a constant velocity $\overrightarrow{v}$ of magnitude 5 m/s and parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with a zero initial speed and a constant acceleration $\overrightarrow{a}$ of magnitude 4 m/$s^2$. What angle $\theta$ between $\overrightarrow{v}$ and the positive direction of the y axis would result in a collision?

1. 

2. 

3. 

4. 

Q. A particle moving with a uniform acceleration travels 24 m and 64 m in the first two consecutive intervals of 4 sec each. Its initial velocity is

1. 
2. 
3. 
4. 

Q. Air stream horizontally past an air plane .the speed over the top surface is 60m/s and that under the bottom surface is 45m/s .the density of air is 1.293 kg/m³ then the diff in pressure is

Q.

A particle leaces the origin with an initial velocity $\overrightarrow{v}$ = ( 3.00 $\hat{i}$ ) m/s and a constant acceleration $\overrightarrow{a}$ = ( - 1.00$\hat{i}-0.500\hat{j}$ ) m/$s^2$ . When it reaches its maximum x coordinate , what are its velocity and position vector?

(i) Position vector U. -10$\hat{j}$

(ii) velocity vector V.4.5$\hat{i}-22.5\hat{j}$

W.4.5$\hat{i}-21.5\hat{j}$

X. -15$\hat{j}$

1. (i) - U, (ii) - V

2. (i) - X, (ii) - W

3. (i) - V, (ii) - X

4. (i) - W, (ii) - X

Q. A particle is projected from the bottom of an inclined plane of inclination ${30}^{\circ }$ (with the horizontal) with speed $40\text{m/s}$ at an angle ${60}^{\circ }$ with the horizontal. The speed of the particle when its velocity vector is parallel to inclined plane is $(g=10{\text{m/s}}^2)$

1. $\frac{40}{\sqrt{3}}\text{m/s}$
2. $20\text{m/s}$
3. $20\sqrt{3}\text{m/s}$
4. $10\text{m/s}$

Q. A projectile has initially the same horizontal velocity as it would acquire if it had moved from rest with uniform acceleration of $3{\text{m/s}}^2$ for $0.5$ min. If the maximum height reached by it is $80\text{m}$, then the angle of projection is ($g=10{\text{m/s}}^2$)

1. ${\tan }^{-1}3$
2. ${\tan }^{-1}\frac{3}{2}$
3. ${\tan }^{-1}\frac{4}{9}$
4. ${\sin }^{-1}\frac{4}{9}$

Q. A particle is projected upwards at an angle $\theta ={45}^{\circ }$ with horizontal from the top of a tower $10\text{m}$ high. Assume the origin is situated at the bottom of the tower and the speed at which the particle is projected is $40\sqrt{2}\text{m/s}$. Find the equation of trajectory of the particle.

1. $y=x-\frac{x^2}{320}$
2. $y=x-\frac{x^2}{320}-10$
3. $y=x-\frac{x^2}{320}+10$
4. $y=x+\frac{x^2}{320}-10$

Q. From the top of a $19.6\text{m}$ high tower, a ball is thrown horizontally. If the line joining the point of projection to the point where it hits the ground, makes an angle of ${45}^{\circ }$ with the horizontal, then the initial velocity of the ball is

1. $9.8\text{m/s}$
2. $4.9\text{m/s}$
3. $14.7\text{m/s}$
4. $2.8\text{m/s}$

Q. The radius vector of a point A relative to the origin varies as $\overrightarrow{r}=at\hat{i}+b{t}^2\hat{j}$ where a and b are positive constants. Find the equation of trajectory.

1. $y=\frac{b}{a^2}{x}^2$
2. $y^2=\frac{b}{a^2}x$
3. $y=\frac{a^2}{b}{x}^2$
4. $\text{none of these}$

Q. A projectile has initially the same horizontal velocity as it would acquire if it had moved from rest with uniform acceleration of $3{\text{m/s}}^2$ for $0.5$ min. If the maximum height reached by it is $80\text{m}$, then the angle of projection is ($g=10{\text{m/s}}^2$)

1. ${\tan }^{-1}3$
2. ${\tan }^{-1}\frac{3}{2}$
3. ${\tan }^{-1}\frac{4}{9}$
4. ${\sin }^{-1}\frac{4}{9}$

Q. A spherical liquid drop of diameter 2 x 10^-4 m is falling with a constant velocity through air under gravity.If the density of liquid is 500 kg/m³ and co-efficient of viscosity of air is 2 x 10^-5 Ns/m² , determine the terminal velocity of the drop and viscous force acting on it. Neglect the density of air (g=9.8 m/s²)