Horizontal and Vertical Components of Projectile Motion

Q. A person moved from $A$ to $B$ on a circular path as shown in figure. If the distance travelled by him is $60\text{m}$, then the magnitude of displacement would be (Given $\cos {135}^{\circ }=–0.7$)

Q. A body is projected up with a velocity equal to ${\left(\frac{3}{4}\right)}^{th}$ to the escape velocity from the surface of the earth. Find the height above earth's surface up to which it reaches. Given R is the radius of the earth.

Q. A particle is projected from the ground at an angle of ${60}^{\circ }$ with the horizontal with speed $u=20\text{m/s}$. The radius of curvature of the path of the particle, when its velocity makes an angle of ${30}^{\circ }$ with the horizontal is ($g=10{\text{m/s}}^2$)

1. $10.6\text{m}$
2. $12.8\text{m}$
3. $15.4\text{m}$
4. $24.2\text{m}$

Q.

A cricket ball is hit at an angle 45° to the horizontal with kinetic energy K the kinetic energy at the highest point is what?

a)k

b)k/2

c)ksin 45°

d)zero

Q. What is escape velocity? What is the derivation for escape velocity?

Q. If an alpha particle and a proton are accelerated from rest by a potential difference of 1 megavolt, then the ratio of their kinetic energy will b

Q.

How can we explain Galileos experiment?

Q.

Which of the following statements is true?

A block slides down a smooth inclined plane when released from the top, while another falls freely from the same point

1. Freely falling block will reach the ground first

2. The sliding block will reach the ground first

3. Both the blocks will reach the ground at the same speed

4. Both the blocks will reach the ground at different speeds

Q.

A boy can throw a stone up to a maximum height of 10m .The maximum horizontal distance that the boy can throw the same stone up to will be

Ans:20

But I calculated it using R/H=4/tan(45)

Since maximum range I took tan45...The answer came out to be 40m ...COuld you please tell me what is wrong with the method I used...

Q. At an angle of ${30}^{\circ }$ to the magnetic meridian, the apparent dip is ${45}^{\circ }$. Find the true dip :

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

Q.

The change of position of an object is called distance.

1. True
2. False

Q. A body is projected vertically up with certain velocity. At point $P$ in its path, the ratio of its potential energy to kinetic energy is $36:64$. The ratio of velocity of projection to velocity at $P$ is

1. $\frac{5}{4}$
2. $\frac{4}{3}$
3. $\frac{9}{4}$
4. $\frac{3}{2}$

Q.

An enemy plane is flying horizontally at an altitude of 2 km with a speed of 300 $m{s}^{-1}.$ An armyman with an anti-aircraft gun on the ground sights the enemy plane when it is directly overhead and fires a shell with a muzzle speed of 600 $m{s}^{-1}$. At what angle with the vertical should the gun be fired so as to hit the plane?

1. ${30}^{\circ }$

2. ${75}^{\circ }$

3. ${60}^{\circ }$

4. ${45}^{\circ }$

Q.

A balloonist releases a bag from a balloon, rising at $40m/s$ at a time when the balloon is $100m$ above the ground. If $g=10m/s^2$, then the bag reaches the ground in

1. $18s$

2. $16s$

3. $10s$

4. $20s$

Q. ntA body of mass 4 kg is moving up an inclined plane rising 1 in 40 with velocity 40m/sec if efficiency is 50% then calculate power required.n

Q.

A bomb is dropped from a plane flying horizontally with uniform speed. Show that the bomb will explode vertically below the plane. Is the statement true if the plane files with uniform speed but not horizonrally ?

Q. Distinguish clearly between distance and displacement of a projectile.

Q. A stone is projected vertically up from the top of a tower at a velocity 9.8 M per second it reaches the foot of the building in 4 seconds what is the height of the tower and velocity of the stone when it reaches the ground

Q. Two particles are projected simultaneously with the same speed $v$ in the same vertical plane with angles of elevation $\theta$ and $2\theta$, where $\theta <{45}^{\circ }$. At what time will their velocities be parallel ?

1. $\frac{v}{g}\cos \left(\frac{\theta }{2}\right)\sin \left(\theta \right)$
2. $\frac{v}{g}\cos \left(\frac{\theta }{2}\right)cosec\left(\frac{3\theta }{2}\right)$
3. $\frac{v}{g}\cos \left(\frac{\theta }{2}\right)\sin \left(\frac{3\theta }{2}\right)$
4. $\frac{v}{g}\cos \left(\frac{\theta }{2}\right)cosec\left(\frac{\theta }{2}\right)$

Q.

A particle is projected from point o with velocity v1 at angle 30 degree with the horizontal and another paeticle is projected from point p which os vertically below the highest point with velocity v2 in the vertical upward direction For two particles to collide ythe raatio v1/v2will be

Q. A projectile is thrown with a speed $u$ at an angle $\theta$ with the vertical. Its average velocity between the instants, it crosses half the maximum height is :

1. $u\cos \theta$, horizontal and in the plane of projection
2. $u\sin \theta$, horizontal and in the plane of projection
3. $2u\cos \theta$, vertical and in the plane of projection
4. $2u\sin \theta$, vertical and in the plane of projection

Q.

A pendulum bob of mass 50 g is suspended from the ceiling of an elevator. Find the tension in the string if the elevator (a) goes up with acceleration 1.2 $m/s^2$, (b) goes up with deceleration 1.2 $m/s^2$, (c) goes up with uniform velocity , (d) goes down with acceleration 1.2 $m/s^2$, (e) goes down with deceleration 1.2 $m/s^2$ and (f) goes down with unifrom velocity.

Q.

Four balls are dropped from the top of a tower at intervals of one second. The first ball reaches the ground after four seconds of dropping. What are the distances between first and second, second and third, third and fourth balls at this instant?

Q.

When a stone is thrown vertically upwards, its velocity is continuously decreased. Why?

Q. Assertion : A negative acceleration of a body can be associated with a ‘slowing down’ of the body.
Reason : Acceleration is a vector quantity.

1. If both assertion and reason are true and the reason is the correct explanation of the assertion.
2. If both assertion and reason are true but reason is not the correct explanation of the assertion.
3. If assertion is true but reason is false.
4. If the assertion and reason both are false.
5. If assertion is false but reason is true.

Q.

an object after travelling in uniform motion for some time , takes a U turn, and traces back its path, with the same constant speed but in opposite direction, will the total motin b uniform motion(bcz we said uniform motion is equal distances(and not displacement) in equal time intervals)

Q. A particle is projected with a velocity $u$, at an angle $\alpha$ with the horizontal. Time at which its vertical component of velocity becomes half of its net speed at the highest point will be

1. $\frac{u}{2g}(\sin \alpha -\cos \alpha )$
2. $\frac{u}{2g}$
3. $\frac{u}{2g}(2\cos \alpha -\sin \alpha )$
4. $\frac{u}{2g}(2\sin \alpha -\cos \alpha )$

Q.

Figure (9-E22) shows a small body of mass m placed over a larger mass M whose surface is horizontal near the smaller mass and gradually curves to become vertical. The smaller mass is pushed on the longer one at a speed v and the system is left to itself. Assume that all the surfaces are frictionless. (a) Find the speed of the larger block when the smaller block is sliding on the vertical part. (b) Find the speed of the smaller mass when it breaks off the larger mass at height h. (c) Find the maximum height (from the ground) that the smaller mass ascends (d) Show that the smaller mass will again land on the bigger one. Find the distance traversed by the bigger block during the time when the smaller block was in its fight under gravity.

Q. A particle is thrown upward with some kinetic energy. Then, what is the characteristic of particle kinetic energy at the highest point?

1. Kinetic energy gets absorbed by the air.
2. Kinetic energy is maximum.

3. Totally kinetic energy gets convert into potential energy.

4. Kinetic energy remains the same.

Q. A circular tube of mass $M$ is placed vertically on a horizontal surface as shown in the figure. Two small spheres, each of mass $m$, just fit in the tube are released from the top, as shown in the figure. If $\theta$ gives the angle between radius vector of either ball with the vertical, obtain the value of the ratio $m/M$ for which the tube breaks its contact with ground when $\theta ={60}^{\circ }$ (Ignore any friction)