Horizontal and Vertical Components of Projectile Motion

Q.

Approximately how many kilometers are represented by $1°$ of latitude.

Q.

If $p,q$and $r$ are any real numbers, then

1. $max(p,q)<max(p,q,r)$

2. $min(p,q)=\left(\frac{1}{2}\right)[p+q–|p–q\left|\right)$

3. $max(p,q)<min(p,q,r)$

4. none of these

Q. A body is projected with a velocity of $30\text{m/s}$ at an angle of ${60}^{\circ }$ to the horizontal. Find the magnitude of velocity when the angle between the velocity vector and acceleration vector is ${120}^{\circ }$.

1. $20\sqrt{3}\text{m/s}$
2. $\frac{20}{\sqrt{3}}\text{m/s}$
3. $10\sqrt{3}\text{m/s}$
4. $\frac{10}{\sqrt{3}}\text{m/s}$

Q. This section contains 1 Assertion-Reason type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.
इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (a), (b), (c) तथा (d) दिये गये हैं, जिनमें से केवल एक सही है।

A : Horizontal range of a ground to ground projectile is same for angle of projection θ and (90° – θ).
A : धरातल से धरातल प्रक्षेप्य की क्षैतिज परास, प्रक्षेपण कोण θ तथा (90° – θ) के लिए समान है।

R : Horizontal range does not depend on angle of projection.
R : क्षैतिज परास, प्रक्षेपण कोण पर निर्भर नहीं करती है।

1. (Both (A) and (R) are true and (R) is the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है
3. (A) is true but (R) is false
   
   (A) सही है लेकिन (R) गलत है
4. (A) is false but (R) is true
   
   (A) गलत है लेकिन (R) सही है

Q. The vertical component of velocity of a projectile is a constant.

1. False
2. True

Q. In projectile motion, there is a constant velocity along the horizontal direction and constant acceleration along the vertical direction.

1. False
2. True

Q.

A fighter plane flying horizontally at an altitude of $1.5\mathrm{km}$ with a speed of $200{\mathrm{ms}}^{-1}$ passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell to hit the plane. The speed of the shell is $600{\mathrm{ms}}^{-1}$. At what minimum altitude should the pilot fly the plane to avoid being hit ? [Take $g=10{\mathrm{ms}}^{-2}$ ]

Q. A projectile is fired with some velocity making certain angle with the horizontal. Which of the following graphs is the best representation for the kinetic energy of a projectile $\left(KE\right)$ versus its horizontal displacement $\left(x\right)$?

1. 
2. 
3. 
4. 

Q. A ball is thrown upwards and it returns to ground describing a parabolic path. Which of the following remains constant

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

Q. Trajectory followed by a particle moving in xy plane is given by y = 4x – 3x², where x, y are in meters. Distance between points where its y coordinate is zero, is

xy तल में गतिमान एक कण द्वारा अनुसरित प्रक्षेप-पथ को y = 4x – 3x² द्वारा व्यक्त किया जाता है, जहाँ x, y मीटर में हैं। उन बिन्दुओं के मध्य दूरी ज्ञात कीजिए, जहाँ इसका y निर्देशांक शून्य है।

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

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

Q. The correct value of dip angle at a place is ${45}^{\circ }$. If the dip circle is rotated by ${45}^{\circ }$ out of the meridian, then the tangent of the angle of apparent dip at the place is

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

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

Q. A body is projected with a velocity of $30\text{m/s}$ at an angle of ${60}^{\circ }$ to the horizontal. Find the magnitude of velocity when the angle between the velocity vector and acceleration vector is ${120}^{\circ }$.

1. $20\sqrt{3}\text{m/s}$
2. $\frac{20}{\sqrt{3}}\text{m/s}$
3. $10\sqrt{3}\text{m/s}$
4. $\frac{10}{\sqrt{3}}\text{m/s}$

Q.

Fill in the blanks using sign $>,<\text{or}=$

$\text{XIX \_\_\_\_}\text{VII}$

Q. A bomb is released from an aeroplane which is moving horizontally with a velocity $196\text{m/s}$ at a height of $980\text{m}$ from the ground. Find the velocity with which the bomb hits the ground.

1. $196\text{m/s}$
2. $138.5\text{m/s}$
3. $240\text{m/s}$
4. $144\text{m/s}$

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

Q.

Fill in the blanks using sign $>,<\text{or}=$

$\text{IV \_\_\_\_}\text{X}$

Q. The speed of a projectile is not constant.

1. True
2. False

Q. A projectile is thrown at $40\sqrt{2}\text{m/s}$ with an angle ${45}^{\circ }$ with horizontal. What will be the magnitude of velocity of the projectile after $1\text{sec}$ of its journey.

1. $30\text{m/s}$
2. $40\text{m/s}$
3. $50\text{m/s}$
4. $60\text{m/s}$

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

Q.

Fill in the blanks using sign $>,<\text{or}=$

$\text{VII \_\_\_\_}\text{XII}$

Q.

Thief A is in an apartment 10m high and is throwing a bag of valuables horizontally at 5 m/s. Thief B is initially standing right below the point of release. Find the velocity with which he should run to catch the bag in time.

1. More than 5 m/s

2. Less than 5m/s

3. at 5 m/s

4. Data insufficient