Introduction to Projectile Motion

Q.

An elevator descends into a mine shaft at the rate of 5 metres per minute. If it begins to descend from 15 metres above the ground, what will be its position after 45 minutes?

Q. A ball rolls off the top of stair way with a horizontal velocity of magnitude $1.8\text{m/s}$. The steps are $0.2\text{m}$ high and $0.2\text{m}$ wide. Which step will the ball hit first?

1. $\text{Second}$
2. $\text{First}$
3. $\text{Third}$
4. $\text{Fourth}$

Q. The escape velocity from a planet is $v_o$. The escape velocity from another planet having twice the radius, but of same density will be -

1. $0.5v_0$
2. $v_0$
3. $2v_0$
4. $4v_0$

Q. The escape velocity corresponding to a planet of mass M and radius R is 50 km/sec. If the planet's mass and radius were 4M and R respectively, then the corresponding escape velocity would be –

1. 100 km/sec
2. 50 km/sec
3. 200 km/sec
4. 25 km/sec

Q.

Trajectory of particle in a projectile motion is given as y = x - $\frac{x^2}{80}$ .

Here , x and y are in meters. For this projectile motion match the following with g = 10 m / $s^2$

"$$\begin{array}{cc}coloumn1& coloumn2\\ \left(a\right)AngleofProjection& \left(p\right)20\\ \left(b\right)Angleofvelocitywithhorizontalafter4s& \left(q\right)80\\ \left(c\right)MaximumHieght& \left(r\right){45}^{\circ }\\ \left(d\right)HorizontalRange& \left(s\right){tan}^{-1}\frac{1}{2}\end{array}$$ "

1. 

2. 

3. 

4. 

Q. A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than ${90}^{\circ }$. If at its extreme position, the string is cut, which of the following trajectory is possible for the bob afterwards?

1. 
2. 
3. 
4. 

Q. An object is launched at a velocity of $20m/s$ in a direction making an angle of ${30}^{\circ }$ upward with the horizontal. What is the total flight time (between launch and touching the ground) of the object?
(Take $g=10m/s^2$)

1. $5s$
2. $2s$
3. $20\sqrt{3}s$
4. $1s$

Q. An object of mass $m$ is at rest on earth's surface. Escape speed of this object is $v_e$. Same object is orbiting earth with $h=R$, then its escape speed will be $v_e^{{}^{\prime }}$. Find the correct alternative

1. $v_e^{{}^{\prime }}=\frac{v_e}{4}$
   
2. $v_e^{{}^{\prime }}=2v_e$
   
3. $v_e^{\prime }=\frac{v_e}{\sqrt{2}}$
   
4. $v_e^{\prime }=\frac{\sqrt{2}{v}_e}{3}$
   

Q. A ground to ground projectile is at point A at t $=\frac{T}{3}$, is at point B at $t=\frac{5T}{6}$ and reaches the ground at $t=T$. The difference in heights between points A and B is

1. $\frac{g{T}^2}{6}$
2. $\frac{g{T}^2}{12}$
3. $\frac{g{T}^2}{18}$
4. $\frac{g{T}^2}{24}$

Q. A ball is thrown from a building $10\text{m}$ tall towards another building $75\text{m}$ away at an initial velocity of $30\text{m/s}$ at an angle of ${30}^{\circ }$ with the horizontal. The height of the other building is also $10\text{m}$. Take $g=10{\text{m/s}}^2$. Choose the correct statement from the options given below:

1. The $Y$ component of the velocity is greater than the $X$ component of the velocity.
2. The ball falls short of the building by $1.728m$.
3. The ball flies over the other building.
4. The ball touches the building $1.728m$ below its original height.

Q.

A man walking downhill with velocity $V_0$ finds that his umbrella gives him maximum protection from rain when he holds it such that the stick is perpendicular to the hill surface. When the man turns back and climbs the hill with velocity $V_0$, he finds that it is most appropriate to hold the umbrella stick vertically. Then the actual speed of raindrops in terms of $V_0$ is: (the inclination of the hill is $\theta =37°$).

1. $\frac{\sqrt{63}}{3}{V}_0$

2. $\frac{\sqrt{73}}{3}{V}_0$

3. $\frac{\sqrt{87}}{3}{V}_0$

4. $\frac{\sqrt{71}}{3}{V}_0$

Q. A ball is thrown upwards. It returns to ground describing a parabolic path. which of the following remains constant?

1. Speed of the ball
2. Kinetic energy of the ball
3. Vertical component of velocity
4. Horizontal component of velocity.

Q.

A particle is projected from the ground. If the equation of the trajectory is y = x - $\frac{x^2}{2}$ , then the time of flight is

1. 

2. 

3. 

4. 

Q. If a projectile is fired with an initial velocity $u$ at an angle $\theta$ from the horizontal, for what time does it remain in the air?

Q. A cricketer hits a ball with a velocity 25 m/s at ${60}^{\circ }$ above the horizontal. How far above the ground it passes over a fielder 50m from the bat (assume the ball is struck very close to the ground)

1. 8.2 m
2. 9.0 m
3. 11.6 m
4. 12.7 m

Q. The radius of a planet is nine times of the radius of earth. Both have almost equal average mass-densities. If $V_P$ and $V_E$ are the escape velocities of the planet and the earth respectively, then

1. $V_E=9V_P$
   
2. $V_E=3V_P$
   
3. $V_P=3V_E$
   
4. $V_P=9V_E$
   

Q. The parabolic path of projectile is Y= $\frac{x}{\sqrt{3}}-\frac{x^2}{60}$ its maximum height is

1. 5 m
2. 10 m
3. 15 m
4. 20 m

Q. A bullet with muzzle velocity $100\sqrt{2}\text{m/s}$ is to be fired at an angle of ${45}^{\circ }$ with the horizontal. Find the coordinates of bullet after $t=4\text{s}$, assuming bullet was initially at origin. Take $g=10{\text{m/s}}^2$.

1. $400\text{m},320\text{m}$
2. $400\text{m},240\text{m}$
3. $140\text{m},290\text{m}$
4. $40\text{m},165\text{m}$

Q. Air planes A and B are flying with constant velocity in the same vertical plane at angles 30${}^{\circ }$ and 60${}^{\circ }$ with respect to the horizontal respectively as shown in figure. The speed of A is 100$\sqrt{3}m{s}^{-1}$. At time t = 0 s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t = $t_0$, A just escapes being hit by B, $t_0$ is:

1. 3 s
2. 2 s
3. 1 s
4. 5 s

Q. A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than ${90}^{\circ }$. If at its extreme position, the string is cut, which of the following trajectory is possible for the bob afterwards?

1. 
2. 
3. 
4. 

Q. The volume of a diatomic gas $(\gamma =7/5)$ is increased two times in a polytropic process with molar heat capacity C = R. How many times will the rate of collision of molecules against the wall of the vessel be reduced as a result of this process ? The answer is $(x{)}^{4/3}times$ then x is

Q. The escape velocity from a planet is $v_0$. The escape velocity from a planet having twice the radius but same density will be?

1. $0.5v_0$
2. $v_0$
3. $2v_0$
4. $4v_0$

Q. The equation of motion of a projectile are given by x = 36 t metre and 2y = 96 t – 9.8 $t^2$ metre. The angle of projection is

1. ${sin}^{-1}$($\frac{4}{5}$)
2. ${sin}^{-1}$($\frac{3}{5}$)
3. ${sin}^{-1}$($\frac{4}{3}$)
4. ${sin}^{-1}$($\frac{3}{4}$)

Q. The equation of motion of a projectile are given by x = 36 t metre and 2y = 96 t – 9.8 $t^2$ metre. The angle of projection is

1. 
2. 
3. 
4. 

Q. A person sitting in the rear end of a 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 height $\left(h_m\right)$ attained and the ranges $\left(R\right)$ seen by the thrower and the outside observer compare each other?

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

Q. A cricketer hits a ball with a velocity 25 m/s at ${60}^{\circ }$ above the horizontal. How far above the ground it passes over a fielder 50m from the bat (assume the ball is struck very close to the ground)

1. 8.2 m
2. 9.0 m
3. 11.6 m
4. 12.7 m

Q. The time of flight of projectile is $10$ second and its range is $500m$. The maximum height reached by will be $(g=10m/s^2)$

1. $25m$
2. $50m$
3. $82m$
4. $125m$

Q. A swimmer wishes to cross $500m$ wide river flowing at $3km/h$. His speed with respect to water is $5km/h$.

1. $20min,20min,20min$
2. $12min,12min,6min$
3. $20min,40min,10min$
4. $30min,20min,15min$

Q. The equation of motion of a projectile are given by x = 36 t metre and 2y = 96 t – 9.8 $t^2$ metre. The angle of projection is

1. ${sin}^{-1}$($\frac{4}{5}$)
2. ${sin}^{-1}$($\frac{3}{5}$)
3. ${sin}^{-1}$($\frac{4}{3}$)
4. ${sin}^{-1}$($\frac{3}{4}$)

Q. A point object of mass M is projected with a speed $10m{s}^{-1}$ at an angle ${60}^o$ with the horizontal. The speed at the highest point of its trajectory is.

1. $5m{s}^{-1}$
2. $Zero$
3. $10m{s}^{-1}$
4. $5\sqrt{3}m{s}^{-1}$
5. $10\sqrt{3}m{s}^{-1}$