Time of Flight with Ground as Frame of Reference

Q.

The position of a body moving along $x$-axis at time $t$ is given by $x=\left(t^2-4t+6\right)m$. The distance traveled by the body in time interval $t=0\text{s}$ to $t=3\text{s}$.

1. $5\text{m}$

2. $7\text{m}$

3. $4\text{m}$

4. $3\text{m}$

Q. On an inclined plane of inclination ${30}^{\circ }$, a ball is thrown at an angle of ${60}^{\circ }$ with the horizontal, from the foot of the incline, with a velocity of $10\sqrt{3}{\text{ms}}^{-1}$. Then, the ball will hit the inclined plane in time: (take $g=10m{s}^{-2}$)

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

Q.

A car made a run of $390km$ in $x$ hours. If the speed had been $4km/hr$ more, it would have taken $2hours$ less for the journey. Find $x$

Q. A projectile is thrown from the base of an incline of ${30}^{\circ }$ as shown in the figure. It is thrown at an angle of ${60}^{\circ }$ from the horizontal direction at a speed of $10\text{m/s}$. The total time of flight is: $(g=10{\text{m/s}}^2)$

1. $\frac{\sqrt{3}}{2}\text{s}$
2. $\frac{2}{\sqrt{3}}\text{s}$
3. $\sqrt{3}\text{s}$
4. $0.5\text{s}$

Q. A projectile s aimed at a target on a horizontal plane but falls 8 m short, when the angle of projection is ${15}^0$, while it overshoots by 16 m, when the angle is ${35}^0$. The angle of projection to hit the target is

1. 
2. 
3. 
4. 

Q. A particle is projected from a point (0, 1) on Y-axis (assume + Y direction vertically upwards) aiming towards a point (4, 9). It fell on ground along x axis in 1 sec. Taking g = 10 $m/s^2$ and all coordinates in metres. Find the X-coordinate where it fell:

1. (3, 0)
2. (4, 0)
3. (2, 0)
4. $(2\sqrt{5},0)$

Q.

A particle is travelling along a straight line $OX$ . The distance $x$ of the particle from $O$ at a time $t$ is given by $x=37+27t–t^3$, where $t$ is time in $second$. The distance of the particle from $O$ when it comes to rest is

1. $81m$

2. $91m$

3. $101m$

4. $111m$

Q. In an electric filed, potential at a point with position vector $\overrightarrow{r}$ is given by $v=\frac{343}{|\overrightarrow{r}|}$. The electric field at $\overrightarrow{r}=3\overrightarrow{i}+2\overrightarrow{j}+6\overrightarrow{k}$ is

1. $21\overrightarrow{i}+14\overrightarrow{j}+42\overrightarrow{k}$
2. $3\overrightarrow{i}+2\overrightarrow{j}+6\overrightarrow{k}$
3. $\frac{3\overrightarrow{i}+2\overrightarrow{j}+6\overrightarrow{k}}{7}$
4. $-(3\overrightarrow{i}+2\overrightarrow{j}+6\overrightarrow{k})$

Q.

A particle is projected at an angle of ${37}^{\circ }$ with an inclined plane as shown in figure. Calculate:

(i) Time of flight of particle.

(ii) Distance traveled by particle (AB) along the inclined plane

1. Time of flight = 2 sec

   Distance along incline = 16 m

2. Time of flight = 3 sec

   Distance along incline = 6 m

3. Time of flight = $\frac{12}{5}$sec

   Distance along incline = $\frac{12}{5}(8-6\sqrt{3})m$

4. Time of flight = $\frac{12}{5}$sec

   Distance along incline = $(8-6\sqrt{3})m$

Q. A particle is projected from a point at the foot of a fixed plane inclined at angle ${45}^{\circ }$ to the horizontal, in the vertical plane containing the line of greatest slope through the point. If $\theta (>{45}^{\circ }$) is the inclination to the horizontal of the initial direction of projection, for what values of $\tan \theta$ will the particle strike the plane horizontally?

Q. A projectile thrown with velocity v making angle $\theta$ with vertical gains maximum height H in the time for which the projectile remains in air, the time period is

1. $\sqrt{H\cos \theta /g}$
2. $\sqrt{2H\cos \theta /g}$
3. $\sqrt{4H/g}$
4. $\sqrt{8H/g}$

Q.

If a particle is projected from point A, normal to the plane calculate

(i) Time of flight?

(ii) AB=?

1. Height of point of projection should be given

2. 

3. 

4. 

Q. A plane is inclined at an angle $\alpha ={30}^{\circ }$ with respect to the horizontal. A particle is projected with a speed $u=2\text{m/s}$, from the base of the plane, as shown in figure. The distance from the base, at which the particle hits the plane, is close to:
(Take $g=10{\text{m/s}}^2$)

1. $20\text{cm}$
2. $\text{180 cm}$
3. $\text{26 cm}$
4. $\text{14 cm}$

Q. A particle is thrown with velocity $u$ making an angle $\theta$ with the vertical. It just crosses the top of two poles each of height $h$ after $1s$ and $3s$ respectively. The maximum height of projectile is-

1. $9.8m$
2. $19.6m$
3. $4.9m$
4. $39.2m$

Q. A javelin thrown into air at an angle with the horizontal has a range of $200m$. If the time of flight is $5s$, then the horizontal component of velocity of the projectile at the highest point of the trajectory is

1. $0$ $m{s}^{-1}$
2. $40$ $m{s}^{-1}$
3. $9.8$ $m{s}^{-1}$
4. $\infty$

Q. A bullet fired at an angle of ${15}^o$ with the horizontal hits the ground $6km$ away. Keeping the same velocity of projection for the bullet to attain a range of $12km$, the angle of projection should be:

1. ${15}^o$
2. ${30}^o$
3. ${60}^o$
4. ${45}^o$

Q. A ball is projected upwards from the top of a tower with a velocity of $50m{s}^{-1}$ making an angle of $30$ with the horizontal. The height of the tower is $70m$. After how much time from the instant of throwing will the ball reach the ground?

1. $7s$
2. $5s$
3. $9s$
4. $2s$

Q. The maximum height attained by a projectile when thrown at an angle $0$ with the horizontal is found to be half the horizontal is found to be half the horizontal range Then is equal to:

Q. The distances covered by a particle thrown in a vertical plane, in horizontal and vertical directions at any instant of time $t$ are $x=3t$ and $y=4t-4t^2$. The range of the particle is

1. $3m$
2. $4m$
3. $2.4m$
4. $5m$

Q. A particle is projected from a point at the foot of a fixed plane inclined at angle ${45}^{\circ }$ to the horizontal, in the vertical plane containing the line of greatest slope through the point. If $\theta (>{45}^{\circ }$) is the inclination to the horizontal of the initial direction of projection, for what values of $\tan \theta$ will the particle strike the plane horizontally?

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

1. $2\sqrt{20}$ m/sec, $60$
2. $20\sqrt{3}$ m/sec, $60$
3. $6\sqrt{40}$ m/sec, $30$
4. $40\sqrt{6}$ m/sec, $30$

Q. A projectile is thrown from the base of an incline of ${30}^{\circ }$ as shown in the figure. It is thrown at an angle of ${60}^{\circ }$ from the horizontal direction at a speed of $10\text{m/s}$. The total time of flight is: $(g=10{\text{m/s}}^2)$

1. $\frac{2}{\sqrt{3}}\text{s}$
2. $\frac{\sqrt{3}}{2}\text{s}$
3. $\sqrt{3}\text{s}$
4. $0.5\text{s}$

Q. The maximum range of projectile is $500m$. If the particle is thrown up a plane, which is inclined at an angle of ${30}^o$ with the same speed, the distance covered by it along the inclined plane will be:

1. $250m$
2. $500m$
3. $750m$
4. $1000m$

Q.

If a particle is projected from point A, normal to the plane calculate

(i) Time of flight?

(ii) AB=?

1. $\frac{T=2sec}{AB=40\sqrt{3}m}$

2. $\frac{T=1sec}{AB=20\sqrt{3}m}$

3. Height of point of projection should be given

4. $\frac{T=4sec}{AB=40\sqrt{3}m}$

Q. A particle is projected from a point at the foot of a fixed plane inclined at angle ${45}^{\circ }$ to the horizontal, in the vertical plane containing the line of greatest slope through the point. If $\theta (>{45}^{\circ }$) is the inclination to the horizontal of the initial direction of projection, for what values of $\tan \theta$ will the particle strike the plane horizontally?

Q.

If a particle is projected from point A, normal to the plane calculate

(i) Time of flight?

(ii) AB=?

1. $\frac{T=2sec}{AB=40\sqrt{3}m}$

2. $\frac{T=1sec}{AB=20\sqrt{3}m}$

3. Height of point of projection should be given

4. $\frac{T=4sec}{AB=40\sqrt{3}m}$

Q. A projectle is fired from a gun at an angle ${45}^o$ with a speed of m/s relative to ground. At the highest point in its flight the explodes into two fragments of equal mass. One fragment comes at rest just after explosion. How far from the gun does the other fragment land, assuming a horizontal ground? Take $g=10m/s^2?$

Q. If Rand H represent the horizontal range and the maximum height achieved by a projectile then which of the relation exists?

1. $\frac{H}{R}=4\cot \theta$
2. $\frac{R}{H}=4\cot \theta$
3. $\frac{H}{R}=4\tan \theta$
4. $\frac{R}{H}=4\tan \theta$

Q. The vertical component of the velocity of projectile is:

1. $3v\sin \theta$
2. $v\sin \theta$
3. $\frac{v\sin \theta }{\sqrt{2}}$
4. $\frac{v\sin \theta }{\sqrt{3}}$

Q. A projectile is aimed at a mark on a horizontal plane through the point of projection and falls $6$m short when its elevation angle is ${30}^o$. The projectile overshoots the mark by $9$m when the angle of projection is ${45}^o$. The correct distance of the mark is?

1. $\frac{(9\sqrt{3}+12)}{2-\sqrt{3}}$m
2. $(30\sqrt{3}+51)m$
3. $(60+30\sqrt{3})m$
4. $30(2-\sqrt{3})m$