Applications of Horizontal and Vertical Components

Q. A ball is projected from the ground with a speed $u$ making an angle $\theta$ with the horizontal. Which of the following graphs correctly represents the variation of angle between the velocity and acceleration vectors with time.
[If $T$ is the time of flight]

1. 
2. 
3. 
4. 

Q.

An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically above a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

1. 1200 m

2. 0.33 km

3. 3.33 km

4. 33 km

Q. A body is projected with a velocity $v$ at an angle of projection $\theta$ with the horizontal. The direction of velocity of the body makes angle ${30}^{\circ }$ with the horizontal at $t=2\text{s}$ and then after further $1\text{s}$, it reaches the maximum height. Then
$(g=10{\text{m/s}}^2)$

1. $v=20\sqrt{3}\text{m/s}$
2. $\theta ={60}^{\circ }$
3. $\theta ={30}^{\circ }$
4. $v=10\sqrt{3}\text{m/s}$

Q. A ball is projected from top of a tower with a velocity of $5m/s$ at an angle of ${53}^{\circ }$ to horizontal. Its speed when it is at a height of $0.35m$ from the point of projection is (Take $g=10m/s^2$)

1. $3m/s$
2. $4m/s$
3. $3\sqrt{2}m/s$
4. Data insufficient

Q. Referring to the above two questions, the acceleration due to gravity is given by

1. $10m/se{c}^2$
2. $5m/se{c}^2$
3. $20m/se{c}^2$
4. $2.5m/se{c}^2$

Q. If a bomb is dropped from a plane flying at constant speed (not horizontally), the bomb will explode vertically below the plane.

1. True
2. False

Q.

A ball whose kinetic energy is E, is thrown at an angle of ${45}^{\circ }$ with the horizontal. Its kinetic energy at the highest point of its trajectory will be

1. E

2. $\frac{E}{\sqrt{2}}$

3. $\frac{E}{2}$

4. Zero

Q. A ball is projected from top of a tower with a velocity of 5 m/s at an angle of ${53}^{\circ }$ to horizontal. Its speed when it is at a height of $0.45m$ from the point of projection is (Take $g=10m/s^2$)

1. 2m/s
2. 3m/s
3. 4 m/s
4. Data insufficient

Q.

A particle P is projected with velocity $u_1$ at an angle of ${30}^{\circ }$ with the horizontal. Another particle Q is thrown vertically upwards with velocity $u_2$ from a point vertically below the highest point of path of P. The necessary condition for the two particles to collide at the highest point is

1. $u_1=u_2$

2. $u_1=2u_2$

3. $u_1=\frac{u_2}{2}$

4. $u_1=4u_2$

Q. A ball is projected with velocity $V_0$ at an angle of elevation ${30}^{\circ }$. Mark the correct statement

1. Kinetic energy will be zero at the highest point of the trajectory
2. Vertical component of momentum will be conserved
3. Horizontal component of momentum will be conserved
4. Gravitational potential energy will be minimum at the highest point of the trajectory

Q.

A particle of mass 100 g is fired with a velocity $20mse{c}^{-1}$ making an angle of ${30}^{\circ }$ with the horizontal. When it rises to the highest point of its path then the change in its momentum is

1. $\sqrt{3}$ $kgmse{c}^{-1}$

2. $\frac{1}{2}kgmse{c}^{-1}$

3. $\sqrt{2}$ $kgmse{c}^{-1}$

4. $1kgmse{c}^{-1}$

Q.

A projectile thrown with an initial velocity $u$ has the same range R when the maximum height attained by it is either $h_1$ or $h_2.$ Then $R,h_1$ and $h_2$ are related as

1. $R=\sqrt{h_1{h}_2}$

2. $R=2\sqrt{h_1{h}_2}$

3. $R=3\sqrt{h_1{h}_2}$

4. $R=4\sqrt{h_1{h}_2}$

Q. A body is released from the top of a tower of height h. It takes t sec to reach the ground. Where will be the ball after time $\frac{t}{2}$ sec

1. At $\frac{h}{2}$ from the ground
2. At $\frac{h}{4}$ from the ground
3. Depends upon mass and volume of the body
4. At $\frac{3h}{4}$ from the ground

Q.

A projectile has a range R and time of flight T. If the range is doubled by increasing the speed of projection, without changing the angle of projection, the time of flight will become

1. $\frac{T}{\sqrt{2}}$

2. $\sqrt{2}T$

3. $\frac{T}{2}$

4. $2T$

Q.

It is possible to project a particle with a given speed in two possible ways so as to have the same range, R. The product of the times taken to reach this point in the two possible ways is proportional to

1. $1/R$

2. R

3. $R^3$

4. $\frac{1}{R^2}$

Q. A particle is projected with velocity 20 m/s at an angle of 30º with horizontal. The time when speed of particle is minimum is [g = 10 m/s²]

एक कण को क्षैतिज के साथ 30º कोण पर 20 m/s के वेग से प्रक्षेपित किया जाता है। कण की चाल किस समय पर न्यूनतम है? [g = 10 m/s²]

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

Q.

A particle of mass 100 g is fired with a velocity $20mse{c}^{-1}$ making an angle of ${30}^{\circ }$ with the horizontal. When it rises to the highest point of its path then the change in its momentum is

1. $\sqrt{3}$ $kgmse{c}^{-1}$

2. $\frac{1}{2}kgmse{c}^{-1}$

3. $\sqrt{2}$ $kgmse{c}^{-1}$

4. $1kgmse{c}^{-1}$

Q. When the ratio of the minimum velocity to the maximum velocity is $\frac{1}{2}$ in a projectile motion, the angle of projection of projectile is?

1. ${60}^{\circ }$
2. ${45}^{\circ }$
3. ${30}^{\circ }$
4. ${15}^{\circ }$

Q.

The horizontal distance x and the vertical height y of a projectile at a time t are given by
$x=atandy=b{t}^2+ct$
where a, b and c are constants. What is the magnitude of the velocity of the projectile 1 second after it is fired?

1. $\sqrt{a^2+(2b+c{)}^2}$

2. $\sqrt{2a^2+(b+c{)}^2}$

3. $\sqrt{2a^2+(2b+c{)}^2}$

4. $\sqrt{a^2+(b+2c{)}^2}$

Q.

An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically above a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

1. 1200 m

2. 0.33 km

3. 3.33 km

4. 33 km

Q. A ball is projected from the ground with velocity $v$ such that its range is maximum
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i. Velocity at half of the maximum height in vertical direction}& a.\frac{v}{2}\\ \text{ii Velocity at the maximum height}& b.\frac{v}{\sqrt{2}}\\ \text{iii. Change in its velocity when it returns}& c.v\sqrt{2}\\ \text{to the ground}& \\ \text{iv. Average velocity when it reaches}& d.\frac{v}{2}\sqrt{\frac{5}{2}}\\ \text{the maximum height}& \end{array}$

1. i- a ii-b iii- d iv- c
2. i- a ii-b iii- c iv- d
3. i- b ii-a iii- d iv- c
4. i- a ii-d iii- b iv- c

Q. A ball is projected from the ground with a speed $u$ making an angle $\theta$ with the horizontal. Which of the following graphs correctly represents the variation of angle between the velocity and acceleration vectors with time.
[If $T$ is the time of flight]

1. 
2. 
3. 
4. 

Q.

A cricketer hits a ball with a velocity 25 m/sat ${60}^{\circ }$above the horizontal. How far above the ground it passes over a fielder 50 mfrom the bat (assume the ball is struck very close to the ground)

1. 8.2 m

2. 9.0 m

3. 11.6 m

4. 12.7 m

Q.

A boy throws a ball with a velocity u at an angle θ with the horizontal. At the same instant he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of :

1. u cos $\theta$

2. u sin $\theta$

3. u tan $\theta$

4. $\sqrt{u^{2}tan\theta }$
   

Q. A ball is projected from top of a tower with a velocity of 5 m/s at an angle of ${53}^{\circ }$ to horizontal. Its speed when it is at a height of $0.45m$ from the point of projection is (Take $g=10m/s^2$)

1. 2m/s
2. 3m/s
3. 4 m/s
4. Data insufficient

Q. A body of mass m is thrown upwards at an angle $\theta$ with the horizontal with velocity v. While rising up the velocity of the mass after t seconds will be

1. $\sqrt{(vcos\theta {)}^2+(vsin\theta {)}^2}$
2. $\sqrt{(vcos\theta -vsin\theta {)}^2-gt}$
3. $\sqrt{v^2+g^2{t}^2-\left(2vsin\theta \right)gt}$
4. $\sqrt{v^2+g^2{t}^2-\left(2vcos\theta \right)gt}$

Q. A ball is thrown from a point with a speed $v_0$ at an angle of projection $\theta$. From the same point and at the same instant , a person starts running with a constant speed $v_0/2$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

1. Yes, ${60}^{\circ }$
2. Yes, ${30}^{\circ }$
3. No
4. Yes, ${45}^{\circ }$

Q. A particle is projected from ground at an angle of ${45}^{\circ }$ with initial speed of $30\sqrt{2}$ m/s. Mass of the body is 500 gram then impulse(in Ns) by gravitational force during flight is

1. 20
2. 30
3. 40
4. 50

Q.

At what angle should a ball be projected up an inclined plane with a velocity so that it may hit the incline normally. The angle of the inclined plane with the horizontal is $\alpha$.

1. $\theta =co{t}^{-1}\left(\frac{1}{2}cot\alpha \right)$

2. $\theta =ta{n}^{-1}\left(\frac{1}{2}cot\alpha \right)$

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

4. $\theta =co{t}^{-1}\left(\frac{1}{2}tan\alpha \right)$

Q.

A particle is projected from a point O with a velocity u in a direction making an angle $\alpha$ upward with the horizontal. After some time at point P it is moving at right angle with its initial direction of projection. The time of flight from O to P is

1. $\frac{usin\alpha }{g}$

2. $\frac{ucosec\alpha }{g}$

3. $\frac{utan\alpha }{g}$

4. $\frac{usec\alpha }{g}$