Applications of Horizontal and Vertical Components

Q.

What is the ratio of the distance traveled by a body falling freely from rest in the first, second, and third seconds of its fall?

Q.

A body is released from the top of a tower of height h. It takes t sec to reach the ground. Where will be the ball after time $\frac{t}{2}$ s.

1. At h/2 from the ground

2. At 3h/4 from the ground

3. At h/4 from the ground

4. Depends upon mass and volume of the body

Q.

A stone is projected from a horizontal plane. It attains maximum height ${}^{\prime }{H}^{\prime }$ & strikes a stationary smooth wall & falls on the ground vertically below the maximum height. Assume the collision to be elastic, the height of the point on the wall where ball will strike is

(Elastic collision means that after colliding on a plane the perpendicular component of the velocity before collision gets reversed after the collision. Here $v_x$ is normal to plane)

1. 

2. None of these

3. 

4. 

Q. A ball of mass m is dropped from height h on a horizontal floor which collides with it with speed u. If coefficient of restitution in floor is e, then impulse imparted to ball by the floor on its second rebounce is(1) meu(2) meu (e + 1)(3) me^2u (e + 1)(4) me^2u (e-1)

Q. A cricket ball is hit at ${30}^0$ with the horizontal with kinetic energy . The kinetic energy at the highest point is

1. Zero
2. 
3. 
4. 

Q.

A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is

1. Equal to the time of fall

2. Less than the time of fall

3. Greater than the time of fall

4. Twice the time of fall

Q.

If a hole is bored along the diameter of the earth and a stone is dropped into hole

1. The stone reaches the other side of the earth and escapes into space

2. The stone reaches the centre of the earth and stops there

3. The stone reaches the other side of the earth and stops there

4. The stone executes simple harmonic motion about the centre of the earth

Q. Three identical balls are connected by light inextensible strings with each other as shown and rest over a smooth horizontal table. At the moment t = 0, ball B is imparted a velocity. Calculate the velocity of A when it collides with ball C.

Q.

The distance through which a body falls in nth second is h. The distance through which it falls in the next second is

1. h

2. h+g/2

3. h-g

4. h+g

Q.

A lamp is $50$ ft. above the ground. A ball is dropped from the same height from a point $30$ ft. away from the light pole. If ball falls a distance $s=16t^2$ ft. in $t$seconds, then the speed of the shadow of the ball moving along the ground $\frac{1}{2}$ s later is

1. $-1500\text{ft/s}$

2. $1500\text{ft/s}$

3. $-1600\text{ft/s}$

4. $1600\text{ft/s}$

Q. 42.a body of mass 10kg is projected with velocity at an angle theta with horizontal at the highest point of trajectory body explodes ijnto 2equal parts if one part retraces its path . find the distance of point from point of projection where body hits the ground

Q. A gun is aimed at a target in line of its barrel. The target is released & allowed to fall under gravity at the same instant the gun is fired. Given sufficient space, the bullets will _____.

1. certainly miss the target

2. pass above the target

3. pass below the target

4. hit the target

Q. 35. A fighter plane pulling out for a dive at a speed of 900km/hr.Assuming its path to be a vertical circle of radius 2000m and its mass to be 16000 kg, find the force exerted by the air on it at the lowest point. Take g=9.8.

Q.

A boy throws up a ball in a stationary lift and the ball returns to his hands in 10 s. Now if the lift starts moving up at a speed of 5 m/s. The time taken for a ball thrown straight up to return to his hands is:

1. more than 10 s

2. insufficient information given

3. less than 10 s

4. equal to 10 s

Q.

At what angle should a ball be projected up an inclined plane with a velocity so that it may hit the incline normally. The angle of the inclined plane with the horizontal is $\alpha$.

1. 

2. 

3. 

4. 

Q. The initial speed of an arrow shot from a bow, at an elevation of ${30}^{\circ }$, is $15{\text{ms}}^{–1}$. Find its velocity when it hits the ground back.

1. $7.5\text{m/sec at}{60}^{\circ }$ clockwise from horizontal
2. $7.5\text{m/sec at}{30}^{\circ }$ clockwise from horizontal
3. $15\text{m/sec at}{30}^{\circ }$ clockwise from horizontal
4. $15\text{m/sec at}{60}^{\circ }$ clockwise from horizontal

Q. A man B standing on a cart throws a ball with speed 2 m/s w.r.t. himself. The cart is moving with a constant speed rightwards. At which angle with velocity of cart should the man B throw the ball relative to himself, such that the ball moves vertically up w.r.t. ground Options: Should have chosen 150° 30° 60° 120°

Q.

A boy throws a ball with a velocity u at an angle θ with the horizontal. At the same instant he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of :

1. 

2. 

3. 

4. 

Q.

A projectile thrown at an angle of ${30}^{\circ }$ with the horizontal has a range $R_1$. Another projectile thrown, with the same velocity, at an angle ${30}^{\circ }$ with the vertical, has a range $R_2$. The relation between $R_1$ and $R_2$ is

1. $R_1=\frac{R_2}{2}$

2. $R_1=R_2$

3. $R_1=2R_2$

4. $R_1=4R_2$

Q. 42. A staircase contains three steps each 10 cm high and20 cm wide (figure 3-E9). What should be the minimumhorizontal velocity of a ball rolling off the uppermostplane so as to hit directly the lowest plane ?Figure 3-E9

Q. {A ball falls on an inclined plane of inclination θ from a height h above the point of impact and makes an inelastic collision with coefficient of restitution e. Where will it hit the plane again}?

Q. Water drops fall at regular intervals from a tap which is above the ground. The third drop is leaving the tap at the instant the first drop touches the ground. How far above the ground is the second drop at that instant

1. 3.75 m
2. 4.00 m
3. 2.50 m
4. 1.25 m

Q. Paragraph for below question

नीचे दिए गए प्रश्न के लिए अनुच्छेद

A projectile is projected with velocity 30 m/s at an angle of 60º with horizontal. At time t = t₀ projectile velocity is perpendicular to its initial velocity. Let speed of projectile at that instant be v, then answer the following question. [g = 10 m/s²]

एक प्रक्षेप्य को क्षैतिज से 60º कोण पर 30 m/s के वेग से प्रक्षेपित किया जाता है। समय t = t₀ पर, प्रक्षेप्य का वेग अपने प्रारम्भिक वेग के लम्बवत् है। माना इस क्षण पर प्रक्षेप्य की चाल v है, तब निम्नलिखित प्रश्नों के उत्तर दीजिए। [g = 10 m/s²]

Q. Value of t₀ is

प्रश्न - t₀ का मान है

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

Q.

Two seconds after projection a projectile is travelling in a direction inclined at ${30}^{\circ }$ to the horizontal after one more sec, it is travelling horizontally, the magnitude and direction of its velocity are

1. $2\sqrt{20}m/sec,{60}^{\circ }$

2. $20\sqrt{3}m/sec,{60}^{\circ }$

3. $6\sqrt{40}m/sec,{30}^{\circ }$

4. $40\sqrt{6}m/sec,{30}^{\circ }$

Q. A stone is projected from level ground at time t = 0, let $v_x$ and $v_y$ be the horizontal and vertical components of velocity at any time t ; x and y are displacements along horizontal and vertical from the point of projection at any time t. Then (Neglect air friction)

1. $v_y-t$ graph is a straight line
2. $x-t$ graph is a straight line passing through origin
3. $y-t$ graph is a straight line passing through origin
4. $v_x-t$ graph is a straight line

Q.

The figure shows two positions A and B at the same height h above the ground. If the maximum height of the projectile is $H$, then determine the time t elapsed between the positions A and B in terms of $H$.

1. $t=\sqrt{\frac{8h}{g}}$

2. $t=\sqrt{\frac{h}{8g}}$

3. $t=\sqrt{\frac{8}{g}(H-h)}$

4. $t=\sqrt{\frac{(H-h)}{8g}}$

Q. 28. A staircase contains three steps having height 10 cm each . If each are 20 cm wide then the the minimum horizontal velocity of a ball moving off plane so as to hit the lowest plane directly is

Q.

A demo CD, 8 cm in diameter, spins 200 rev/min. Determine its linear velocity in cm/s for a point 3 cm from the center.

1. 62.8 cm/s

2. 20.9 cm/s

3. 20/6 cm/s

4. 40π/6 cm/s

Q. A ball is thrown from a point with a speed $v_0$ at an angle of projection $\theta$. From the same point and at the same instant , a person starts running with a constant speed $v_0/2$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

1. Yes, ${60}^{\circ }$
2. Yes, ${30}^{\circ }$
3. No
4. Yes, ${45}^{\circ }$

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

A ball projected with velocity $\overrightarrow{v}=\left(3\hat{i}+6\hat{j}\right)m/s$ from origin, moves in x-y plane. Ground is taken as x-z plane and g = 10 m/s², then

मूल बिन्दु से वेग $\overrightarrow{v}=\left(3\hat{i}+6\hat{j}\right)m/s$ से प्रक्षेपित एक गेंद x-y तल में गति करती है। धरातल को x-z तल के रूप में लिया जाता है तथा g = 10 m/s², तब

1. Equation of path followed by the ball is 9y = 18x – 5x²
   
   गेंद द्वारा अनुसरित पथ का समीकरण 9y = 18x – 5x² है
2. Time of flight of the ball is 2 s
   
   गेंद का उड्डयन काल 2 s है
3. Horizontal range of the ball is 3.6 m
   
   गेंद की क्षैतिज परास 3.6 m है
4. Time of flight of the ball is 1.2 s
   
   गेंद का उड्डयन काल 1.2 s है