Range

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. 1 : 2

2. 2 : 1

3. 1 : 4

4. 4 : 1

Q.

Distance between a frog and an insect on a horizontal plane is $9m$. Frog can jump with a maximum speed of $\sqrt{10}m/s$ . Minimum number of jumps required by the frog to catch the insect is (Take $g=10m/s^2$)

1. 8

2. 9

3. 7

4. 4

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 particle is projected under gravity at an angle of projection ${45}^{\circ }$. If for ground projectile motion its range is 36m. Find maximum Height attained by particle in S I units is

1. 9

2. 8

3. 7

4. 6

Q.

A ball is thrown upwards at an angle of ${60}^{\circ }$ to the horizontal. It falls on the ground at a distance of 90 m. If the ball is thrown with the same initial velocity at an angle ${30}^{\circ }$, it will fall on the ground at a distance of

1. 30 m

2. 60 m

3. 90 m

4. 120 m

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. R

4. S

Q. An electric dipole has a fixed dipole moment $\overrightarrow{p}$, which makes angle $\theta$ with respect to $x-$ axis. When system is subjected to an electric field $\overrightarrow{E_1}=E\hat{i},$ it experiences a torque $\overrightarrow{{\tau }_1}=-\tau \hat{k}$. When subjected to another electric field $\overrightarrow{E_2}=\sqrt{3}E\hat{j}$, it experiences a torque $\overrightarrow{{\tau }_2}=-\overrightarrow{{\tau }_1}$. The angle $\theta$ is

1. ${90}^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$
4. ${30}^{\circ }$

Q. On seeing enemy ships at a distance of 125$\sqrt{3}$ m from the shore the cannons start firing fireballs. If the cannons fire at a speed of 50 m/s then at what angle should they aim so they do not miss. Also at what angle can the cannons achieve the maximum distance?

1. Angle to destroy ships = 45°; Angle for maximum range = 90°

2. Angle to destroy ships = 30°; Angle for maximum range = 45°

3. Angle to destroy ships = 60°; Angle for maximum range = 45°

4. Angle to destroy ships = 90°; Angle for maximum range = 90°

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. $\frac{R}{2}$

3. $R$

4. $4R$

Q. An electric dipole has a fixed dipole moment $\overrightarrow{p}$, which makes angle $\theta$ with respect to $x-$ axis. When system is subjected to an electric field $\overrightarrow{E_1}=E\hat{i},$ it experiences a torque $\overrightarrow{{\tau }_1}=-\tau \hat{k}$. When subjected to another electric field $\overrightarrow{E_2}=\sqrt{3}E\hat{j}$, it experiences a torque $\overrightarrow{{\tau }_2}=-\overrightarrow{{\tau }_1}$. The angle $\theta$ is

1. ${45}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$
4. ${90}^{\circ }$

Q.

A ball is thrown from ground level of a field with a speed of 12.0 m/s at an angle of ${45}^{\circ }$ with the horizontal. At what distance will it hit the field again? Take g = 10.0 m/$s^2$.

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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 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 $\frac{v_0}{2}$ 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 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. 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. $1:\sqrt{3}$
4. $\sqrt{3}:1$

Q.

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

1. 100 m

2. 200 m

3. 400 m

4. 800 m

Q. On seeing enemy ships at a distance of 125$\sqrt{3}$ m from the shore the cannons start firing fireballs. If the cannons fire at a speed of 50 m/s then at what angle should they aim so they do not miss. Also at what angle can the cannons achieve the maximum distance?

1. Angle to destroy ships = ${45}^{\circ }$; Angle for maximum range = ${90}^{\circ }$
2. Angle to destroy ships = ${30}^{\circ }$; Angle for maximum range = ${45}^{\circ }$
3. Angle to destroy ships = ${60}^{\circ }$; Angle for maximum range = ${45}^{\circ }$
4. Angle to destroy ships = ${90}^{\circ }$; Angle for maximum range = ${90}^{\circ }$