Summary for Time, Height and Range

Q. The horizontal range of a projectile is $4\sqrt{3}$ times its maximum height. Its angle of projection will be

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

Q.

The greatest height to which a man can throw a stone is h. The greatest distance to which he can throw it, will be

1. $\frac{h}{2}$

2. $2h$

3. $3h$

4. $h$

Q.

A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following

1. Straight path

2. Circular path

3. Parabolic path

4. Hyperbolic path

Q. A projectile is thrown with an initial velocity of $v=a\hat{i}+b\hat{j}$ if the range of projectile is double the maximum height reached by it then

1. a = 2b
2. b = a
3. b = 2a
4. b = 4a

Q. The horizontal range is four times the maximum height attained by a projectile. The angle of projection is

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

Q. During a projectile motion, if the maximum height equals the horizontal range, then the angle of projection with the horizontal is

1. ${\text{tan}}^{-1}2$
2. ${\text{tan}}^{-1}1$
3. ${\text{tan}}^{-1}3$
4. ${\text{tan}}^{-1}4$

Q. A charged cork ball of mass 1 g is suspended on a light string in the presence of a uniform electric field as shown. When $\overrightarrow{E}=(3\hat{i}+5\hat{j})\times {10}^{5}N{C}^{-1}$, the ball is in equilibrium at $\theta =37$. T is the tension in the string and q is the charge on the ball (Take sin 37 = 0.60 and $g=10m{s}^{-2}$)

1. Q = 21 nC
2. q = 12 nC
3. $T=5.55\times {10}^{-3}N$
4. $T=4.55\times {10}^{-3}N$

Q. A particle is projected with velocity $u$ at angle ${\theta }_1$ with horizontal. The ratio of range and maximum height is $4$.
When it is projected at angle ${\theta }_2$ with horizontal with same speed, the ratio of range and maximum height is $2$.
Then $\frac{\tan {\theta }_1}{\tan {\theta }_2}$ will be equal to

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

Q. In the given figure point A and C are on the horizontal ground & A and B are in same vertical plane. Simultaneously bullets are fired from A, B and C and they collide at D. The bullet at B is fired horizontally with speed of $\frac{72}{5}$ km/hr and the bullet at C is projected vertically upward at velocity of $\frac{54}{5}$ km/hr. Find velocity of the bullet projected from A in m/s.

Q.

A popular game in Indian village is goli which is played with small glass balls called golis. The goli of one player is situated at a distance of 2.0 m from the goli of the second player. This second played has to project his goli by keeping the thumb of the left hand at the place of his goli, holding the goli between his two middle fingers and making the throw, if the projected goli hits the goli of the first player, the second player wins. If the height from which the goli projected is 19.6 m from the ground and the goli is to be projected horizontally, with what speed should it be projected so that it directly hits the stationary goli without falling on the ground earlier.

Q.

The angle of projection at which the horizontal range and maximum height of projectile are equal is

1. ${45}^{\circ }$

2. $\theta =ta{n}^{-1}\left(0.25\right)$

3. $\theta =ta{n}^{-1}4or(\theta ={76}^{\circ })$

4. ${60}^{\circ }$

Q. A boy throws a water-filled balloon at an angle of ${53}^{\circ }$ with a speed of $10m/s$. A car is advancing towards the boy at a constant speed of $5m/s$. If the balloon is to hit the car, how far away should the car be when the balloon is thrown? $(g=10m{s}^{-2})$

1. $8m$
2. $9.6m$
3. $15.6m$
4. $17.6m$

Q. A projectile is thrown with a velocity of $50m{s}^{-1}$ at an angle of ${53}^o$ with the horizontal. The equation of the trajectory is given by (Take $g=10m/s^2$)

1. $180y=240x-x^2$
2. $180y=x^2-240x$
3. $180y=135x-x^2$
4. $180y=x^2-135x$

Q. A body is thrown from a point with speed $50\text{m/s}$ at an angle ${37}^{\circ }$ with horizontal. When it has moved a horizontal distance of $80\text{m}$ then its distance from point of projection is

1. $40\text{m}$
2. $40\sqrt{2}\text{m}$
3. $40\sqrt{5}\text{m}$
4. None

Q. A projectile is projected with a kinetic energy K. Its range is R. It will have the minimum kinetic energy, after covering a horizontal distance equal to

1. 0.25 R
2. 0.5 R
3. 0.75 R
4. R

Q.

At what point of a projectile motion acceleration and velocity are perpendicular to each other

1. At the topmost point

2. At the point of projection

3. At the point of drop

4. Any where in between the point of projection and topmost point

Q. A ball is projected vertically upwards its speed at half of maximum height is 20 m/s what is the maximum height attained by it

Q.

A body starts slipping down an incline and moves half meter in half second. How long will it take to move the next half meter?

Q. A projectile projected from the ground has its direction of motion making an angle 45 with the horizontal at a height 40 m its initial velocity of projection is 50 M per second the angle of projection is?

Q.

For a projectile, the ratio of maximum height reached to the square of flight time is $(g=10m{s}^{-2})$

1. 5 : 4

2. 5 : 2

3. 5 : 1

4. 10 : 1

Q.

A stone is just released from the window of a train moving along a horizontal straight track. For anstationaryobserver on the ground, the stone will hit the ground following

1. Straight path

2. Parabolic path

3. Hyperbolic path

4. Circular path

Q. A projectile is thrown with initial velocity of 20 m/s at an angle of ${37}^o$ from horizontal. Time after which velocity becomes perpendicular to acceleration is

1. 
   1.2 sec
2. 
   0.5 sec
3. 
   0.6 sec
4. 
   2.4 sec

Q. A trolley having a cannon fixed to it which can shoot only vertically, is moving with a velocity $v_0=12\text{m/sec}$ in horizontal direction. At a certain instant, it is at a distance of $120\text{m}$ from a balloon which is held on ground and now it is released. The balloon starts rising with constant velocity $2v_0$. Calculate the minimum velocity(in $\text{m/s}$) of cannon ball so that it can hit the balloon.

Q. A particle is projected with velocity 2gh such that it crosses two walls of height h separated by 2h .What is the angle of projection?

Q. Find the average velocity of a projectile between the instants it crosses one third of the maximum height. It is projected with $u$ making an angle $\theta$ with the vertical.

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

Q. A body is thrown with the velocity $u$ at an angle $\theta$ with the horizontal. If the body remains in air for 6 seconds, the maximum height reached by the body will be

1. $19.6\text{m}$
2. $9.8\text{m}$
3. $20.0\text{m}$
4. $44.1\text{m}$

Q.

The trajectory of a projectile in a vertical plane is $y=\alpha x-\beta x^2$, where $\alpha$ and $\beta$ are constants and $x$ and $y$, are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $H$ are respectively given by

1. ${\tan }^{-1}\left(\alpha \right)$, $\frac{{\alpha }^2}{4\beta }$

2. ${\tan }^{-1}\left(\beta \right)$, $\frac{{\alpha }^2}{2\beta }$

3. ${\tan }^{-1}\left(\frac{\beta }{\alpha }\right)$, $\frac{{\alpha }^2}{\beta }$

4. ${\tan }^{-1}\left(\alpha \right)$, $\frac{4{\alpha }^2}{\beta }$

Q. During a projectile motion, if the maximum height equals the horizontal range, then the angle of projection with the horizontal is

1. ${\text{tan}}^{-1}1$
2. ${\text{tan}}^{-1}2$
3. ${\text{tan}}^{-1}3$
4. ${\text{tan}}^{-1}4$

Q. Relation between pressure (P) and average kinetic energy per unit volume of gas (E) is then?

1. $P=\frac{2}{3}$E.
2. $P=\frac{1}{3}$E
3. $P=\frac{1}{2}$E
4. $P=3$E

Q. An airplane has to go from a point $\text{A}$ to another point $\text{B}$ due ${45}^{\circ }$ east of north. Wind is blowing due north at speed of $200\sqrt{2}\text{km/h}$. The steering-speed of the plane is $400\text{km/h}$. Find the direction in which the pilot should head the plane so as to reach the point $\text{B}$.

1. ${75}^{\circ }$east of north.
2. ${30}^{\circ }$east of north.
3. ${60}^{\circ }$east of north.
4. ${15}^{\circ }$east of north.