Application of Projectile to a Height

Q. A body is thrown horizontally from the top of a tower of height 5 m. It touches the ground at a distance of 10 m from the foot of the tower. The initial velocity of the body is (g = 10 $m{s}^{-2}$)

1. $2.5m{s}^{-1}$
2. $5m{s}^{-1}$
3. $10m{s}^{-1}$
4. $20m{s}^{-1}$

Q.

A bomber plane moves horizontally with a speed of 500 m/s and a bomb released from it, strikes the ground in 10 sec. Angle at which it strikes the ground will be $(g=10m/s^2)$

1. 

2. 

3. 

4. 

Q. A body is projected horizontally from the top of a cliff with a velocity of $9.8m/s$. How much time elapses before horizontal and vertical velocity becomes equal in magnitude? ( Take $g=9.8m{s}^{-2}$)

1. 9.8 $s$
2. 2 $s$
3. 1 $s$
4. 10 $s$

Q. A bomb is dropped on an enemy post by an aeroplane flying with a horizontal velocity of 60 km/hr and at a height of 490 m. How far the aeroplane must be from the enemy post at time of dropping the bomb, so that it may directly hit the target. $(g=9.8m/s^2)$

1. 
2. 
3. 
4. 

Q. A ball is allowed to fall from top of a building . If t1 is time taken to fall first 1/4 th of its height and t2 is time taken to fall last 1/4 th of its height then t2/t1 is

Q. An object $\text{A}$ is kept fixed at the point $x=3\text{m}$ and $y=1.25\text{m}$ on a plank $\text{P}$. At time $t=0$, the plank starts moving along the $+x$ - direction with an acceleration $1.5{\text{m/s}}^2$. At the same instant, a stone is project from the origin with a velocity $\overrightarrow{u}$ as shown. A stationary person on the ground observes the stone hitting the object during its downward motion at an angle of ${45}^{\circ }$ to the horizontal. All the motions are in $x-y$ plane. The velocity $\overrightarrow{u}$ is

1. $(6.25\hat{i}-3.75\hat{j})\text{m/s}$
2. $(6.25\hat{i}+3.75\hat{j})\text{m/s}$
3. $(3.75\hat{i}+6.25\hat{j})\text{m/s}$
4. $(3.75\hat{i}-6.25\hat{j})\text{m/s}$

Q.

At the height 80 m, an aeroplane is moving with 150 m/s. A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped (given g = 10 $m/s^2$)

1. 600 m

2. 605.3 m

3. 80 m

4. 230 m

Q. A ball is thrown upwards at an angle of 60 with horizontal. It falls on the ground at a distance of 90m.If the ball is thrown with the same initial velocity at an angle 30, it will fall on the ground at a distance of

Q. A stone is projected from a point on the ground in such a direction as to hit a bird on the top of a telegraph post of height $h$ and then attain the maximum height $3h/2$ above the ground. If at the instant of projection, the bird were to fly away horizontally with uniform speed, find the ratio between the horizontal velocities of the bird and the stone if the stone still hits the bird while descending. Take $\sqrt{3}=1.73$.

Q. A body of mass 2 gm is projected horizontally from the top of tower of height 20m with a velocity 10 m/s. The charge on the body is 2C. Electric field is a;;lied vertically downwards and of intensity ${10}^{-2}$ N/C. Find the time taken by the body to touch the ground (g = 10 $m/s^2$)

1. 1 sec
2. 1.414 sec
3. 2.828 sec
4. 2 sec

Q. An aeroplane is flying at a height of 1960 m in horizontal direction with a velocity of 360 km/hr. When it is vertically above the point. A on the ground, it drops a bomb. The bomb strikes a point B on the ground, then the time taken by the bomb to reach the ground is

1. 
2. 
3. 
4. 

Q. A gun is mounted on a plateau $960\text{m}$ away from it’s edge as shown. Height of plateau is $960\text{m}$. The gun can fire shells with a velocity of $100\text{m/s}$ at any angle. Of the following choices, what is the minimum distance $\left(OP\right)x$ from the edge of plateau where the shell of gun can reach?

Q. A pendulum bob of mass m is suspended at rest. A constant horizontal force $F=\frac{mg}{2}$ starts acting on it. The maximum angular deflection of the string is

1. ${90}^{\circ }$
2. ${60}^{\circ }$
3. ${53}^{\circ }$
4. ${37}^{\circ }$

Q. The potential energy of a particle varies with distance $x$ as shown in the graph. The force acting on the particle is zero at

1. $A$ and $D$
2. $C$
3. $B$
4. $B$ and $C$

Q.

A body is thrown horizontally from the top of a tower of height 5 m. It hits the ground at a distance of 10 m from the foot of the tower. The initial velocity of the body is (g = 10 m$s^{-2}$)

1. 2.5 ms^-1

2. 5 ms^-1

3. 10 ms^-1

4. 20 ms^-1

Q. A projectile is fired from the bottom of incline plane of inclination ${37}^{\circ }$ at speed of $20$ m/s at an angle $\theta$ with incline plane as shown in figure. If time of flight is $3$ sec, then distance `AB` is $[g=10m/s^2]$

1. $0$ m
2. $12$ m
3. $17$ m
4. $21$ m

Q. A gun is aimed at a target in line of its barrel. The target is released and allowed to fall under gravity at the same instant the gun is fired. Given sufficient space, the bullet will--------[explain clearly ]

Q. A body is thrown horizontally with velocity $\sqrt{2gh}$ from the top of a tower of height h. It strikes the level ground through the foot of tower at a distance x from the tower. The value of x is

1. 
2. 
3. 
4. 

Q. The decrease in the value of $g$ (wrt earth's surface) on going to a height $\frac{R}{2}$ above the earth’s surface will be?

1. $\frac{g}{2}$
2. $\frac{5g}{9}$
3. $\frac{4g}{9}$
4. $\frac{g}{3}$

Q. Two cars $\text{A}$ and $\text{B}$ are moving with uniform speeds as shown in the figure given below, at $t=0$. Find out the shortest distance between the two cars.

1. $2\sqrt{5}\text{m}$
2. $4\sqrt{5}\text{m}$
3. $8\sqrt{5}\text{m}$
4. $6\sqrt{5}\text{m}$

Q. A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same speed how much high above the ground can the cricketer throw the same ball?

1. 50 m
2. 100 m
3. 150 m
4. 200 m

Q. A block of mass $m$ is placed on a wedge of mass $m$ and inclination $\theta$. All surfaces are smooth. Find the acceleration of the wedge.

1. $\frac{mg{\cos }^2\theta }{M+m{\sin }^2\theta }$
2. $\frac{mg{\sin }^2\theta }{M+m{\cos }^2\theta }$
3. $\frac{mg\sin \theta \cos \theta }{M+m{\cos }^2\theta }$
4. $\frac{mg\sin \theta \cos \theta }{M+m{\sin }^2\theta }$

Q.

A gun is aimed at a target in a line of its barrel. The target is released and allowed to fall under gravity at the same instant the gun is fired. The bullet will

1. Hit the target

2. Pass above the target

3. Pass below the target

4. Certainly miss the target

Q. A ball is rolled off the edge of a horizontal table at a speed of 4 m/second. It hits the ground after 0.4 second. Which statement given below is true

1. It hits the ground at a horizontal distance 1.6 m from the edge of the table
2. The speed with which it hits the ground is 4.0 m/second
3. Height of the table is 0.8 m
4. It hits the ground at an angle of 60^o to the horizontal

Q. From the given data, can you find average speed?
A stone is dropped from the top of a tower. When it crosses a point 5 m below the top, another stone is let fall from a point 25 m below the top. Both stones reach the bottom of the tower simultaneously. Find the height of the tower. Take g = 10$m/s^2$.

Q. A projectile is given an initial velocity of$(\hat{i}+2\hat{j})\text{m/s}$, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g=10{\text{m/s}}^2$, the equation of its trajectory is :

1. $4y=2x-5x^2$
2. $y=2x-5x^2$
3. $4y=2x-25x^2$
4. $y=x-5x^2$

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

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

Q. An aeroplane, when it is vertically above the point $A$ on the ground, drops a bomb which hits target $B$ on the ground. If the plane is moving at a height of $1.96km$ from the ground with a speed of $300m/s$, then distance between $A$ and $B$ is (neglecting air resistance)

1. $3km$
   
2. $6km$
   
3. $4m/s$
   
4. $3m/s$
   

Q. A particle is projected from the ground at an angle of $\theta$ with the horizontal with an initial speed of $u$. Find the final velocity when it is perpendicular to the initial velocity.

1. $u\tan \theta$
2. $u\cot \theta$
3. $u\sin \theta$
4. $u\cos \theta$

Q.

An aeroplane flying 490 m above ground level at 100 m/s, releases a block. How far on ground will it strike

1. 0.1 km

2. 1 km

3. 2 km

4. None