Projectile Time, Height and Range

Q. 65. Out of the following representing motion of a particle which represents SHM? 1.x=sin³ wt 2.x=1+wt+w²t² 3.x=coswt + cos3wt + cos5wt 4.x=sinwt+coswt Click here to view details:

Q. The maximum height of an oblique projectile is $8\text{m}$. The horizontal range is $24\text{m}$. The vertical component of the velocity of projection is

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

Q. A ball is projected from point $A$ with velocity $10\text{m/s}$ perpendicular to the inclined plane as shown in figure. Range of the ball on the inclined plane is equal to $\frac{N}{3}\text{m}$. Then, $N$ is equal to

1. $40$
2. $20$
3. $12$
4. $60$

Q. A particle is projected so as to graze the top of two walls each of height $20m$. The walls are at distances of $30m$ and $170m$ respectively from the point of projection. Find the angle of projection.

1. ${\tan }^{-1}\left(\frac{2}{3}\right)$
2. ${\tan }^{-1}\left(\frac{40}{51}\right)$
3. ${\tan }^{-1}\left(1\right)$
4. ${\tan }^{-1}\left(\frac{4}{5}\right)$

Q. The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m s ¯¹ can go without hitting the ceiling of the hall ?

Q. Trajectories of two projectiles are shown in figure. Let $T_1$ and $T_2$ be the time periods and $u_1$ and $u_2$ their speeds of projection. Then

1. $T_1=T_2$
2. $T_1>T_2$
3. $T_1<T_2$
4. Can not say

Q. Two bodies are thrown at angle $\theta$ and $(90-\theta )$ from the same point with same velocity $25m{s}^{-1}$. If the difference between their maximum height is $15m$, find the respective maximum heights.
$(g=10m{s}^{-2})$

1. $H_1=\frac{85}{8}m$ and $H_2=\frac{175}{8}m$
2. $H_1=\frac{185}{8}m$ and $H_2=\frac{65}{8}m$
3. $H_1=\frac{65}{4}m$ and $H_2=\frac{135}{8}m$
4. $H_1=\frac{125}{4}m$ and $H_2=\frac{65}{8}m$

Q. A ball is thrown from a point on a ground at some angle of projection. At the same time, a bird starts from a point directly above this point of projection at a height $h$, horizontally with speed ${}^{\prime }{u}^{\prime }$. Given that during its flight, the ball just touches the bird at only one point. Find the distance on the ground from the point of projection where the ball strikes.

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

Q. The trajectory of a projectile near the surface of the earth is given as $y=2x-9x^2$. Then choose the correct option(s): [Take $g=10{\text{m/s}}^2$]

1. Angle of projection is ${\sin }^{-1}\left(\frac{1}{\sqrt{5}}\right)$
2. Angle of projection is ${\cos }^{-1}\left(\frac{1}{\sqrt{5}}\right)$
3. Speed of projection is $\frac{3}{5}\text{m/s}$
4. Speed of projection is $\frac{5}{3}\text{m/s}$

Q. Ratio of minimum kinetic energies of two projectiles of same mass is $4:1$. The ratio of the maximum height attained by them is also $4:1$. The ratio of their ranges would be

1. $16:1$
2. $4:1$
3. $8:1$
4. $2:1$

Q. The trajectory of a projectile in a vertical plane is given by $y=ax-b{x}^2,$ where $a$ and $b$ are constants and $x$ and $y$ are respectively horizontal and vertical distances of the projectile from the point of projection. The maximum height attained by the particle and the angle of projection from the horizontal are

1. $\frac{b^2}{2a},{\tan }^{-1}\left(b\right)$
2. $\frac{a^2}{b},{\tan }^{-1}\left(2a\right)$
3. $\frac{a^2}{4b},{\tan }^{-1}\left(a\right)$
4. $\frac{2a^2}{b},{\tan }^{-1}\left(a\right)$

Q. The velocity at the maximum height of a projectile is $\frac{1}{2}$ times its initial velocity of projection $\left(u\right)$. Its range on the horizontal plane is

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

Q. A ball rolls off the top of a staircase with a horizontal velocity u. If each step has a height h and a width b, then the ball will just bit the nth step, if n equals

1. 
2. 
3. 
4. 

Q. A boy standing on a long railroad car throws a ball straight upwards with a speed of $10\text{m/s}$ at $t=0$ when the car starts moving on a horizontal road with an acceleration of $1{\text{m/s}}^2$. How far behind the boy will the ball fall on the car? (Take $g=10{\text{m/s}}^2$).

1. $4\text{m}$
2. $2\text{m}$
3. $4.5\text{m}$
4. $8\text{m}$

Q. A man is travelling on a flatcar which is moving up a plane that is inclined at angle $\theta$ to the horizontal with a speed of $5\text{m/s}$ $(\cos \theta =\frac{4}{5})$. He throws a ball towards a stationary hoop located above the incline in such a way that the ball moves parallel to the slope of the incline while going through the centre of the hoop. The centre of the hoop is $4\text{m}$ high from the man's hand, perpendicular to the incline. The time taken (in seconds) by the ball to reach the hoop is [Take $g=10{\text{m/s}}^2$]

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Q. An aircraft moving with a speed of $540\text{km/h}$ is at a height of $6000\text{m}$, just overhead of an anti aircraft gun. If the muzzle velocity of the bullet is $300\text{m/s}$, the firing angle $Q$ from the horizontal for the bullet to hit the aircraft should be

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${37}^{\circ }$

Q. If $R$ and $h$ represent the horizontal range and maximum height respectively of an oblique projectile, then $\frac{R^2}{8h}+2h$ represents

1. Maximum horizontal range
2. Maximum verticle range
3. Time of flight
4. Velocity of projectile at highest point.

Q. The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m/s can go without hitting the ceiling of the hall ?

Q.

Rain is falling vertically with the speed of 60 m/s. A man rides a bicycle with the speed of 20 m/s in east to west direction. What is the direction in which he should hold the umbrella?

1. sin^-1 1/3

2. cos^-1 1/3

3. tan^-1 1/3

4. tan^-1 2/3

Q. A player kicks a football at an angle of ${45}^{\circ }$ with a velocity of $20m{s}^{-1}$. A second player on the goal line $60m$ away in the direction of kick starts running to receive the ball at that instant. Find the speed $\left(m/s\right)$ of the second player with which he should run to strike the ball before it strikes the ground $(g=10m{s}^{-2})$

1. $2\sqrt{2}$
2. $\sqrt{2}$
3. $3\sqrt{2}$
4. $5\sqrt{2}$

Q. A fighter plane flying horizontally at an altitude of $1.5km$ with speed $720km/h$ passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed $600m{s}^{-1}$ to hit the plane ? At what minimum altitude should the pilot fly the plane to avoid being hit ? ($Takeg=10m{s}^{-2}$)

Q. Equation of trajectory of a projectile is given by $y=-x^2+10x$ where $x$ and $y$ are in meters and $x$ is along horizontal and $y$ is vertically upward and particle is projected from origin. Then which of the following options is/are correct?
$(g=10m/s^2)$

1. Initial speed of particle is $\sqrt{505}m/s$
2. Horizontal range is $10m$
3. Maximum height is $25m$
4. Angle of projection with horizontal is ${\tan }^{-1}\left(5\right)$

Q. The maximum height reached by projectile is $4\text{m}$. The horizontal range is $12\text{m}$. Velocity of projection in $\left({\text{ms}}^{-1}\right)$ is
($g$ is acceleration due to gravity)

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

Q. A jet of water is projected at an angle $\theta ={45}^{\circ }$ with the horizontal from a point which is at a distance of $x=15\text{m}$ from a vertical wall as shown in the figure. If the speed of projection is $10\sqrt{2}\text{m/s}$, find out the height from ground at which the water jet strikes vertical wall. Take $g=10{\text{m/s}}^2$

1. $5\text{m}$
2. $3.75\text{m}$
3. $7.5\text{m}$
4. $2.5\text{m}$

Q. The friction coefficient between a road and the type of a vehicle is 4/3. Find the maximum incline the road may have so that once had brakes are applied and the wheel starts skidding, the vehicle going down at a speed of 36 km/hr is stopped within 5 m.

Q. A train is moving along a straight line with a constant acceleration. A boy standing inside the train throws a ball in forward direction with a speed of $10\text{m/s}$ at an angle of ${60}^{\circ }$ to the horizontal, with respect to himself. The boy has to move forward by $1.15\text{m}$ inside the train to catch the ball (at the initial height). If the train starts from rest when the ball is thrown, then
[Take $g=10{\text{m/s}}^2$]

1. Acceleration of train is $5{\text{m/s}}^2$
2. Acceleration of ball is $10{\text{m/s}}^2$
3. Acceleration of ball is $5\sqrt{5}{\text{m/s}}^2$
4. Displacement of train is $8.66\text{m}$

Q. A person sitting at the rear end of the compartment throws a ball towards the front end. The ball follows a parabolic path. The train is moving with uniform velocity of $20m{s}^{-1}$. A person standing outside on the ground also observes the ball. How will the maximum heights $\left(h_m\right)$ attained and the range $\left(R\right)$ seen by the thrower and the outside observer compared to each other?

1. Same $h_m$ and different $R$
2. Same $h_m$ and $R$
3. Different $h_m$ and same $R$
4. Different $h_m$ and $R$

Q. A projectile is thrown with a speed of $100m/s$ making an angle of ${60}^{\circ }$ with the horizontal. Find the minimum time after which its inclination with the horizontal is ${45}^{\circ }$.

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

Q. When the ratio of the minimum velocity to the maximum velocity is $\frac{1}{\sqrt{2}}$ in a projectile motion, the angle of projection of projectile is

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

Q. Suppose the block of the previous problem is pushed down the incline with a force of 4 N. How far will the block move in the first two seconds after starting from rest? The mass of the block is 4 kg.