Applications of Horizontal and Vertical Components

Q. Water drops fall at regular intervals from a tap which is 5m above the ground. The third drop is leaving the tap at the instant the first drop touches the ground. How far above the ground is the second drop at that instant

1. 1.25 m
2. 2.50 m
3. 3.75 m
4. 4.00 m

Q. Two balls $A$ and $B$ are placed at the top of $180m$ tall tower. Ball $A$ is released from the top at $t=0s$. Ball $B$ is thrown vertically down with an initial velocity $u$ at $t=2s$. After a certain time, both balls meet $100m$ above the ground. Find the value of $u$ in $m{s}^{-1}$ [ use $g=10m/s^2$ ]

Q.

A projectile is fired with velocity $u$ making angle $\theta$ with the horizontal. What is the change in velocity when it is at the highest point

1. $ucos\theta$

2. $u$

3. $usin\theta$

4. $(ucos\theta -u)$

Q. An $\text{L-shaped}$ object, made of thin rods of uniform mass density, is suspended with a string as shown in the figure. If $AB=BC$, and the angle made by $AB$ with downward vertical is $\theta$, then:

1. $\tan \theta =\frac{1}{3}$
2. $\tan \theta =\frac{1}{2}$
3. $\tan \theta =\frac{2}{\sqrt{3}}$
4. $\tan \theta =\frac{1}{2\sqrt{3}}$

Q.

A man is sitting on the shore of a river. He is in the line of a 1.0 m long boat and is 5.5 m away from the center of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for successful shot. Assume that the point of Projection and the edge of the boat are in the same horizontal level.

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. 12.7 m

2. 8.2 m

3. 9.0 m

4. 11.6 m

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 body of mass 0.5 kg is projected under gravity with a speed of 98 m/s at an angle of ${30}^{\circ }$ with the horizontal. The change in momentum (in magnitude) of the body is

1. 24.5 N–s

2. 49.0 N–s

3. 98.0 N–s

4. 50.0 N–s

Q.

A projectile can have the same range $R$ for two angles of projection. if $t_1$ & $t_2$ be the times of flight in the two cases then what is the product of the two times of flight?

Q.

The speed of a projectile at the highest point becomes $\frac{1}{\sqrt{2}}$times its initial speed. The horizontal range of the projectile will be

1. 

2. 

3. 

4. 

Q. Two seconds after projection a projectile is travelling in a direction inclined at ${30}^{\circ }$ to the horizontal after one more sec, it is travelling horizontally, the magnitude and direction of its initial velocity are-

1. $20\sqrt{3}\text{m/s},{60}^{\circ }$
2. $6\sqrt{40}\text{m/s},{30}^{\circ }$
3. $40\sqrt{6}\text{m/s},{30}^{\circ }$
4. $2\sqrt{20}\text{m/s},{60}^{\circ }$

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. The initial speed of an arrow shot from a bow, at an elevation of ${30}^{\circ }$, is $15{\text{ms}}^{–1}$. Find its velocity when it hits the ground back.

1. $7.5\text{m/sec at}{30}^{\circ }$ clockwise from horizontal
2. $15\text{m/sec at}{30}^{\circ }$ clockwise from horizontal
3. $7.5\text{m/sec at}{60}^{\circ }$ clockwise from horizontal
4. $15\text{m/sec at}{60}^{\circ }$ clockwise from horizontal

Q.

The aeroplane is shown here on level flight at an altitude of $0.5\mathrm{km}$ and at a speed of $150{\mathrm{kmh}}^{-1}$.

At what distance $x$ should it release a bomb to hit the target? [Take $g=10{\mathrm{ms}}^{-2}$]

1. $150\mathrm{m}$

2. $420\mathrm{m}$

3. $2000\mathrm{m}$

4. $800\mathrm{m}$

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. 

2. 

3. 

4. 

Q. A car is moving horizontally along a straight line with a uniform velocity of $25{\text{ms}}^{-1}$. A projectile is to be fired from this car in such a way that it will return to it after the car has moved by $100\text{m}$. The speed of the projection relative to car (in $m{s}^{-1}$) must be
(Take $g=10{\text{ms}}^{-2}$)

Q. A ball is projected horizontally from top of a $80\text{m}$ deep well with velocity $10\text{m/s}$. Then the ball will fall to the bottom at a distance of (the speed of the ball does not change in any collision)

1. $5\text{m}$ from $A$
2. $5\text{m}$ from $B$
3. $2\text{m}$ from $A$
4. $2\text{m}$ from $B$

Q.

A body is projected up a smooth inclined plane (length = $20\sqrt{2}m$ ) with velocity u from the point M as shown in the figure. The angle of inclination is ${45}^{\circ }$ and the top is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of v

1. 

2. 

3. 

4. 

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 $5m/s$ 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.

The speed of projection of a projectile is increased by 5%, without changing the angle of projection. The percentage increase in the range will be

1. 7.5%

2. 10%

3. 5%

4. 2.5%

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 projectile thrown at an angle of ${30}^{\circ }$ with the horizontal has a range $R_1$. Another projectile thrown, with the same velocity, at an angle ${30}^{\circ }$ with the vertical, has a range $R_2$. The relation between $R_1$ and $R_2$ is

1. $R_1=\frac{R_2}{2}$

2. $R_1=R_2$

3. $R_1=2R_2$

4. $R_1=4R_2$

Q. A balloon of mass 'm' is decending down with an acceleration 'a'. How much mass should be removed from it so that it starts moving up with an acceleration 'a'

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. R

2. $1/R$

3. $R^3$

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

Q. A ball is projected from the point O with velocity 20 m/s at an angle of ${60}^{\circ }$ with horizontal as shown in figure. At highest point of its trajectory it strikes a smooth plane of inclination ${30}^{\circ }$ at point A. The collision is perfectly inelastic. The maximum height from the ground attained by the ball is $\frac{75}{k}$ meter. Find the value of k? (g = 10 $m/s^2$) ___

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. a bomb is projected and explodes at highest point into two equal masses. The first piece returns at the point of projection then what is the distance travelled by the second piece if range is R

Q.

A projectile has a range $\text{R}$ and time of flight $\text{T}$. 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. 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. $2.5m/se{c}^2$