Range

Q. A body of mass $1\text{kg}$ is projected with velocity $50\text{m/s}$ at an angle of ${30}^{\circ }$ with the horizontal. At the highest point of its path, a force $10\text{N}$ starts acting on body for $5s$ vertically upwards besides gravitational force. What is horizontal range of the body ? ($g=10{\text{m/s}}^2$):

1. $125\sqrt{3}\text{m}$
2. $200\sqrt{3}\text{m}$
3. $500\text{m}$
4. $250\sqrt{3}\text{m}$

Q. A projectile can have the same range $R$ for two angles of projection. If $T_1$ and $T_2$ be times of flight in two cases, then the product of the two times of flight is directly proportional to

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

Q. The range of a projectile for a given initial velocity is maximum when the angle of projection is ${45}^{\circ }$. The range will be minimum, if the angle of projection is

1. ${75}^{\circ }$
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${180}^{\circ }$

Q.

A projectile is projected with initial velocity $(6\hat{i}+8\hat{j})m/sec.Ifg=10m{s}^{-2}$, then horizontal range is

1. 4.8 metre

2. 9.6 metre

3. 19.2 metre

4. 14.0 metre

Q. A stone projected at an angle of ${60}^{\circ }$ from the ground level strikes at an angle of ${30}^{\circ }$ on the roof of a building of height ‘h’. Then the speed of projection of the stone is

1. $\sqrt{2gh}$
2. $\sqrt{3gh}$
3. $\sqrt{gh}$
4. $\sqrt{6gh}$

Q.

The maximum horizontal range of a projectile is 400 m. The maximum value of height attained by it will be

1. 200 m

2. 100 m

3. 400 m

4. 800 m

Q. The maximum range of a projectile is $22\text{m}$. When it is thrown at an angle of ${15}^{\circ }$ with the horizontal, its range will be-

1. $22\text{m}$
2. $6\text{m}$
3. $15\text{m}$
4. $11\text{m}$

Q.

A projectile fired with initial velocity u at some angle $\theta$ has a range R. If the initial velocity be doubled at the same angle of projection, then the range will be

1. $2R$

2. $R$

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

4. $4R$

Q.

A bullet fired at an angle of $30$ degrees with the horizontal hits the ground $3km$ away. By adjusting its angle of projection, can one hope to hit a target $5km$ away? Assume the muzzle speed to be fixed, and neglect air resistance.

Q.

An object is thrown along a direction inclined at an angle of ${45}^{\circ }$ with the horizontal direction. The horizontal range of the particle is equal to

1. Vertical height

2. Twice the vertical height

3. Thrice the vertical height

4. Four times the vertical height

Q.

When a particle is projected at an angle to the horizontal, it has range R and time of flight t1. If the same projectile is projected with the same speed at another angle to have the same range and time of flight $t_2$ then,

1. $t_1+t_2=\frac{2R}{g}$

2. $t_1,t_2=\frac{2R}{g}$

3. $t_1-t_2=\frac{2R}{g}$

4. $t_1{t}_2=\frac{2R}{g}$

Q. If a body A of mass M is thrown with velocity V at an angle of ${30}^{\circ }$ to the horizontal and another body B of the same mass is thrown with the same speed at an angle of ${60}^{\circ }$ to the horizontal. The ratio of horizontal range of A to B will be

1. $1:3$
2. $1:1$
3. $\sqrt{3}:1$
4. $1:\sqrt{3}$

Q.

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths accoding to initial horizontal velocity component, highest first

1. 1, 2, 3, 4

2. 2, 3, 4, 1

3. 3, 4, 1, 2

4. 4, 3, 2, 1

Q.

Four bodies P, Q, R and S are projected with equal velocities having angles of projection ${15}^{\circ },{30}^{\circ },{45}^{\circ }and{60}^{\circ }$ with the horizontal respectively. The body having shortest range is

1. P

2. Q

3. S

4. R

Q.

If the range of a gun which fires a shell with muzzle speed V is R , then the angle of elevation of the gun is

1. $co{s}^{-1}\left(\frac{V^2}{Rg}\right)$

2. $\frac{1}{2}\left(\frac{V^2}{Rg}\right)$

3. $\frac{1}{2}si{n}^{-1}\left(\frac{gR}{V^2}\right)$

4. $co{s}^{-1}\left(\frac{gR}{V^2}\right)$

Q.

Two particles A & B are projected with same speed so that the ratio of their maximum height reached is 3:1. If the speed of A is doubled without altering other parameters, the ratio of their horizontal ranges is

1. 1:1

2. 2:1

3. 4:1

4. 3:2

Q.

A projectile is thrown into space so as to have maximum horizontal range R. Taking the point of projection as origin, the co-ordinates of the point where the speed of the particle is minimum are

1. 

2. 

3. 

4. 

Q. A particle thrown at angle ${45}^{\circ }$ with horizontal with speed $u$ has its range equal to $R$. At what angle should it be thrown with same speed for its range to be half of its initial value.

1. ${15}^{\circ }$
2. ${60}^{\circ }$
3. ${70}^{\circ }$
4. ${30}^{\circ }$

Q. The ratio of escape velocities of two planets, if $g$ value on the two planets are $9.9{\text{m/s}}^2$ and $3.3{\text{m/s}}^2$ and their radii are $6400\text{km}$ and $3200\text{km}$ respectively is

1. $2:1$
2. $\sqrt{6}:1$
3. $\sqrt{3}:1$
4. $1:2$

Q. The range of a particle when thrown at angle of ${15}^{\circ }$ with the horizontal is 1.5 km. What maximum range can the particle achieve if speed of projection is kept constant?

1. 1.5 km

2. 3.0 km

3. 6 km

4. 0.75 km

Q. A golfer standing on level ground hits a ball with a velocity of $u=52\text{m/s}$ at an angle $a$ above the horizontal. If $\tan a=\frac{5}{12}$, then the time ( in second upto two decimals) for which the ball is at least $15\text{m}$ above the ground will be (take $g=10{\text{m/s}}^2$)

Q. A particle is projected with a velocity $v$ such that its range on horizontal plane is twice the greatest height attained by it. The range of the projectile will be ($g$ is the acceleration due to gravity).

1. $\frac{4v^2}{5g}$
2. $\frac{4g}{5v^2}$
3. $\frac{v^2}{g}$
4. $\frac{4v^2}{\sqrt{5}g}$

Q.

An object is projected at an angle of ${45}^{\circ }$ with the horizontal. The horizontal range and the maximum height reached will be in the ratio.

1. 2 : 1

2. 1 : 4

3. 1 : 2

4. 4 : 1

Q.

A projectile thrown with a speed vat an angle $\theta$has a range Ron the surface of earth. For same vand $\theta$, its range on the surface of moon will be

1. $6R$

2. $\frac{R}{36}$

3. $36R$

4. $\frac{R}{6}$

Q.

A boy playing on the roof of a 10m high building throws a ball with a speed of 10 m/s at an angle of ${30}^{\circ }$ with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground $(g=10m/s^2,sin{30}^{\circ }=\frac{1}{2},cos{30}^{\circ }=\frac{\sqrt{3}}{2})$

1. 8.66 m

2. 2.60 m

3. 5.20 m

4. 4.33 m

Q. By properly combining two prisms made of different materials, it is possible to-

1. Have dispersion without average deviation
2. Have deviation without dispersion
3. Have both dispersion and average deviation
4. Have neither dispersion nor average deviation

Q. It is raining vertically downwards with the velocity of $3km{h}^{-1}$. A man walks in the rain with a velocity of $4km{h}^{-1}$. The rain drops will be falling on the man with a relative velocity of

1. $5km{h}^{-1}$
2. $1km{h}^{-1}$
3. $3km{h}^{-1}$
4. $4km{h}^{-1}$

Q.

A particle covers 50 m distance when projected with an initial speed. On the same surface it will cover a distance, when projected with double the initial speed

1. 100 m

2. 150 m

3. 200 m

4. 250 m

Q. A player kicks a football at an angle of ${45}^{\circ }$ with a velocity of $30m{s}^{-1}$. A second player $120m$ away along the direction of kick starts running to receive the ball at that instant. Find the speed with which second player should run to reach the ball before it hits the ground $(g=10m{s}^{-2})$

1. $4\sqrt{2}m/s$
2. $5m/s$
3. $5\sqrt{2}m/s$
4. $10\sqrt{2}m/s$

Q. From a canon mounted on a wagon at a height $H$ from the ground, a shell is fired horizontally with a velocity $v_0\text{m/s}$ with respect to canon. The canon and wagon have a combined mass of $M\text{kg}$ and can move freely on the frictionless, horizontal surface. Find the horizontal distance (in $\text{metres}$) between shell and canon, when the shell touches ground.

1. $v_0\sqrt{\frac{2H}{g}}$
2. $\frac{v_{0}m}{M+m}\sqrt{\frac{2H}{g}}$
3. $\frac{v_{0}M}{m}\sqrt{\frac{2H}{g}}$
4. $\frac{v_{0}m}{M}\sqrt{\frac{2H}{g}}$