Frames of Reference

Q. A man wants to reach point $B$ on the opposite bank of a river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point $B$?

1. $\sqrt{2}u$
2. $\frac{u}{\sqrt{2}}$
3. $\sqrt{3}u$
4. $\frac{u}{\sqrt{3}}$

Q. The velocities of a particle in SHM at positions $x_1$ and $x_2$ are $v_1$ and $v_2$ respectively, its time period will be -

1. $2\pi \sqrt{(v_1^2-v_2^2)/(x_2^2-x_1^2)}$
2. $2\pi \sqrt{(x_1^2+x_2^2)/(x_2^2-x_1^2)}$
3. $2\pi \sqrt{(x_1^2-x_2^2)/(v_2^2-v_1^2)}$
4. $2\pi \sqrt{(x_1^2+x_2^2)/(v_2^2+v_1^2)}$

Q.

A juggler throws balls into the air. He throws one whenever the previous one is at its highest point. How high do the balls rise if he throws n balls in each second. Acceleration due to gravity is g.

Q. Two trains one of length $100\text{m}$ and another of length $125\text{m}$, are moving in mutually opposite directions along parallel lines, meet each other, each with speed $100\text{m/s}$. If their accelerations are $0.3{\text{m/s}}^2$ and $0.2{\text{m/s}}^2$ respectively, then the time they take to pass each other will be

1. $5s$
2. $20s$
3. $10s$
4. $15s$

Q. The trajectory of the projectile near the surface of the earth is given as $y=2x-9x^2.$ If it was launched at an angle ${\theta }_0$ with speed $v_0$ then $(g=10{\text{m/s}}^2)$

1. ${\theta }_0={\sin }^{-1}\frac{1}{\sqrt{5}}\text{and}{v}_0=\frac{3}{5}{\text{ms}}^{-1}$
2. ${\theta }_0={\cos }^{-1}\frac{2}{\sqrt{5}}\text{and}{v}_0=\frac{3}{5}{\text{ms}}^{-1}$
3. ${\theta }_0={\cos }^{-1}\frac{1}{\sqrt{5}}\text{and}{v}_0=\frac{5}{3}{\text{ms}}^{-1}$
4. ${\theta }_0={\sin }^{-1}\frac{2}{\sqrt{5}}\text{and}{v}_0=\frac{3}{5}{\text{ms}}^{-1}$

Q. A particle is projected upwards with a velocity of $100\text{m/sec}$ at an angle of ${60}^{\circ }$ with the vertical. Find the time when the particle will move perpendicular to its initial direction taking $g=10{\text{m/sec}}^2$.

1. $2\text{sec}$
2. $4\text{sec}$
3. $10\text{sec}$
4. $20\text{sec}$

Q. In which case, can velocity be negative? displacement be negative?

Q.

A body is thrown vertically up with a velocity u.if it passes 3 points A, B, C in its upward journey with the velocity U/2, U/3, U/4 respectively. The ratio of separation AB and BC is?

Q. a boat streams in a river with velocity 2i cap+5j cap with respect to ground.the river water flows with a velocity of -3icap-4jcap with respect to the ground. what is the relative velocity of boat w.r.t. river water ?

Q. An elevator without a ceiling is ascending up with an acceleration of $5{\text{ms}}^{-2}$. A boy on the elevator shoots a ball in vertical upward direction from a height of $2\text{m}$ above the floor of elevator. At this instant the elevator is moving up with a velocity of $10{\text{ms}}^{-1}$, and the floor of the elevator is at a height of $50\text{m}$ from the ground. The initial speed of the ball is $15{\text{ms}}^{-1}$ with respect to the elevator. Consider the duration for which the ball strikes the floor of elevator in answering following questions. ($g=10{\text{ms}}^{-2}$)

1. $2.13\text{s}$
2. $2.0\text{s}$
3. $3.12\text{s}$
4. $1.0\text{s}$

Q. Two cars start out simultaneously from a point in the same direction, one of them going at a speed of $50$ $km/hr$ and the other at $40$ $km/hr$. In half an hour a third car starts out from the same point and overtakes the first car $1.5$ hours after catching up with the second car. The speed of the third car is

1. $55km/hr$
   
2. $90km/hr$
   
3. $72km/hr$
   
4. $60km/hr$

Q.

A railway train 100 m long passes over a bridge 400 m long at the rate of 72 $\frac{km}{h}$.How long will the train take to cross the bridge ?

Q. Two trains $P$ and $Q$ are moving along parallel tracks with same uniform speed of $\frac{20m}{s}$. The driver of train $P$ decides to overtake train $Q$ and accelerates his train by $\frac{1m}{s^2}$. After $50s,$ train $p$ crosses the engine of train $Q$. Find out what was the distance between the two trains initially provided the length of each train is $400m.$

1. $400m$
2. $480m$
3. $350m$
4. $450m$

Q. Which of the following do not depend on frame of reference?
1. Mass
2. Distance between two points
3. Velocity
4. Distance

1. $1\text{and}2$
2. $2\text{and}3$
3. $1\text{and}4$
4. $1\text{and}3$

Q. A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south.

1. 30° with downstream
2. 60° with downstream
3. 120° with downstream
4. South

Q.

A 100 m long train moving with a constant speed of 90 $\frac{km}{hr}$ crosses a tunnel of 300 meters long. The time taken by the train to cross the tunnel completely is

1. 16 sec

2. 8 sec

3. 4 sec

4. 2 sec

Q.

An airplane flying horizontally at a constant speed of 350 km/h over level ground releases a bundle of food supplies. Ignore the effect of the air on the bundle.What are the bundle’s initial (a) vertical and (b) horizontal components of velocity? (c) What is its horizontal component of velocity just before hitting the ground? (d) If the airplane’s speed were, instead, 450 km/h, would the time of fall be longer, shorter, or the same?

Q. A truck is moving with a constant velocity of $54\text{km/h}$. In which direction (angle with the direction of motion of truck) should a stone be projected up with a velocity of $20\text{m/s}$ relative to truck, so that for a person standing on the earth stone appears to be at right angles to the truck ?

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

Q.

A particle starts from the origin at t = 0 s with a velocity of and moves in the x-y plane with a constant acceleration of .

(a) At what time is the x-coordinate of the particle 16 m? What is the y-coordinate of the particle at that time?

(b) What is the speed of the particle at the time?

Q. Choose the correct option.
i. There is nothing like "Absolute rest" or "Absolute motion".
ii. Frame of reference is attached with observer.
iii. Time does not depends on the frame of reference.
iv. To know the complete information about any event, there is no requirement of observer.

1. i and iv
2. i, ii and iii
3. i and ii
4. i, ii, iii and iv

Q.

A person walking in a compartment of a stationary train is ___ relative to the compartment and is___ relative to the platform.

Q. A body is projected with an initial velocity of $20\hat{i}+20\hat{j}$. It clears a wall at a distance of 20 m. Find the velocity when it clears the wall.

1. 20i + 10j
2. 20i – 10j
3. 15i + 10j
4. 20i + 15j

Q. A ball of mass 0.1kg and moving with velocity 40 m per second strike up that and returned back in the opposite direction with the same speed. Calculate the change in linear movement of the ball.

Q.

The earth takes 24 h to rotate once about its axis. How much time does the sun take to shift by 1º when viewed from the earth?

1. 1 min

2. 5 min

3. 10 min

4. 4 min

Q. A partical is moving in the xy-plane has velocity components dx/dt =2t and dy/dt=4. If the partical start from the origin at t=0 , magnitude of its displacement at t=2s is

Q. 18. An object is moving with speed 10 m/s along the direction of a vector 4i-3j. Velocity of the object is (1) 8i-6j m/s  (2) 10i-10j m/s  (3) 40i-30j m/s  (4) 6i-8j m/s

Q.

When do we say that a body is at rest when do we say that it is moving?

Q. An object may appear moving to one person and at rest to another person at the same time Justify giving an example.

Q.

A bus travels at a speed of 75 km/h to cover a distance of 375 km. What is the time taken by the bus to complete its journey?

Q. How are the states of rest and motion relative?