Motion in a plane — DPP 2

20 NEET questions from Motion in a plane, with answers and explanations. Attempt it as a timed test to get scoring, accuracy breakdown and mistake tracking.

Attempt this test free 20 questions · 30 minutes · +80 marks
1
A unit vector in the direction of resultant vector of $\vec { A } = - 2 \hat { i } + 3 \hat { j } - \hat { k }$ and $\vec { B } = \hat { i } + 2 \hat { j } - 4 \hat { k }$ is:
  1. A $\frac { - 2 \hat { \mathrm { i } } - \hat { \mathrm { j } } + \hat { \mathrm { k } } } { \sqrt { 6 } }$
  2. B $\frac { 2 \hat { \mathrm { i } } + \hat { \mathrm { i } } + \hat { \mathrm { k } } } { \sqrt { 6 } }$
  3. C $\frac{-\hat{\mathrm{i}}+5 \hat{\mathrm{j}}-5 \hat{\mathrm{k}}}{\sqrt{51}}$
  4. D $\frac{2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}$
Show answer & explanation

Correct answer: C

Motion in a plane – NEET-17990
2
If the vectors $\overline { \mathrm { A } } = \hat { \mathrm { i } } + 2 \hat { \mathrm { j } } + 4 \hat { \mathrm { k } }$ and $\overline { \mathrm { B } } = 5 \hat { \mathrm { i } }$ represents the two sides of a triangle, then the third side of the triangle has length?
  1. A $\sqrt { 56 }$
  2. B $\sqrt { 21 }$
  3. C 5
  4. D 6
Show answer & explanation

Correct answer: A

Motion in a plane – NEET-17988
3
A car is moving at a speed of 40 m/s on a circular track of radius 400 m. This speed is increasing at the rate of 3 m/s$^{2}$. The acceleration of car is;
  1. A $4 \mathrm {~m} / \mathrm { s } ^ { 2 }$
  2. B $7 \mathrm {~m} / \mathrm { s } ^ { 2 }$
  3. C $5 \mathrm {~m} / \mathrm { s } ^ { 2 }$
  4. D $3 \mathrm {~m} / \mathrm { s } ^ { 2 }$
Show answer

Correct answer: C

4
Rain is falling vertically with a speed of 35 ms$^{–1}$. Winds starts blowing after some time with a speed of 12 ms$^{–1}$ in the east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?
  1. A $\sin ^{-1}\left(\frac{12}{15}\right)$
  2. B $\cos ^{-1}\left(\frac{12}{35}\right)$
  3. C $\tan ^{-1}\left(\frac{12}{35}\right)$
  4. D $\cot ^{-1}\left(\frac{12}{35}\right)$
Show answer & explanation

Correct answer: C

Motion in a plane – NEET-18003
5
A river is flowing from west to east with a speed $5 \mathrm {~ms} ^ { - 1 }$. A swimmer can swim in still water at speed of $10 \mathrm {~ms} ^ { - 1 }$. If he wants to start from point A on south bank and reach opposite point B on north bank, in what direction should he swim?
  1. A $30 ^ { \circ }$ east of north
  2. B $60 ^ { \circ }$ east of north
  3. C $30 ^ { \circ }$ west of north
  4. D $60 ^ { \circ }$ west of north
Show answer & explanation

Correct answer: C

Motion in a plane – NEET-18000
6
A projectile is given an initial velocity of $( \hat { i } + 2 \hat { j } ) \mathrm { m } / \mathrm { s }$. If $\mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$. Find the equation of trajectory.
  1. A $Y = X - 5 X ^ { 2 }$
  2. B $Y = 2 X - 5 X ^ { 2 }$
  3. C $4 Y = 2 X - 5 X ^ { 2 }$
  4. D $4 Y = 2 X - 25 X ^ { 2 }$
Show answer & explanation

Correct answer: B

$\begin{array}{l}\vec{u}=\hat{i}+2 \hat{j} \\ |\vec{u}|=\sqrt{1+4}=\sqrt{5} \mathrm{~m} / \mathrm{s} \\ Y=X \tan \theta-\frac{g X^{2}}{2 u^{2}}\left(1+\tan ^{2} \theta\right) \quad\left[\tan \theta=\frac{u_{y}}{u_{x}}=\frac{2}{1}=2\right] \\ Y=X \times 2-\frac{10 X^{2}}{2 \times(\sqrt{5})^{2}}\left[1+2^{2}\right]\end{array}$
$Y=2 X-\frac{10 X^{2}}{10}[5]=2 X-5 X^{2}$
Therefore, option (B) is the correct answer.
7
In vector diagram shown in figure where $( \bar { R } )$ is the resultant of vectors $( \bar { A } )$ and $( \bar { B } )$.
Motion in a plane – NEET-17962 If $R = \frac { B } { \sqrt { 2 } }$, then value of angle θ is :
  1. A $30 ^ { \circ }$
  2. B $45 ^ { \circ }$
  3. C $60 ^ { \circ }$
  4. D $75 ^ { \circ }$
Show answer

Correct answer: B

8
Forces 3 N, 4 N, and 12 N act at a point in mutually perpendicular directions. The magnitude of the resultant force is:
  1. A 19 N
  2. B 13 N
  3. C 11 N
  4. D 5 N
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Correct answer: B

9
A fighter plane flying horizontally at an altitude of 1.5 km with a speed of 720 km h$^{–1}$ passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s$^{–1}$ to hit the plane? (Take g = 10 m s$^{–2}$)
  1. A $\sin ^{-1}\left(\frac{1}{3}\right)$
  2. B $\sin ^{-1}\left(\frac{2}{3}\right)$
  3. C $\cos ^{-1}\left(\frac{1}{3}\right)$
  4. D $\cos ^{-1}\left(\frac{2}{3}\right)$
Show answer & explanation

Correct answer: A

Motion in a plane – NEET-17997
10
A fighter plane is flying horizontally at an altitude of 1.5 km with speed 720 kmhr. At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target? (Take $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ )
  1. A $\tan ^ { - 1 } \left( \frac { \sqrt { 3 } } { 4 } \right)$
  2. B $\tan ^ { - 1 } \left( \frac { 3 } { 4 } \right)$
  3. C $\tan ^ { - 1 } \left( \frac { 4 } { \sqrt { 3 } } \right)$
  4. D $\tan ^ { - 1 } \left( \frac { 4 } { 3 } \right)$
Show answer & explanation

Correct answer: A

Motion in a plane – NEET-17996
11
For a given velocity, a projectile has the same range R for two angles of projection, if $t _ { 1 }$ and $t _ { 2 }$ are the times of flight in the two cases then
  1. A $t _ { 1 } t _ { 2 } \propto R ^ { 2 }$
  2. B $t _ { 1 } t _ { 2 } \propto R$
  3. C $t _ { 1 } t _ { 2 } \propto \frac { 1 } { R }$
  4. D $t _ { 1 } t _ { 2 } \propto \frac { 1 } { R ^ { 2 } }$
Show answer

Correct answer: B

12
Two vectors $\bar { A }$ and $\bar { B }$ are such that $\bar { A } + \bar { B } = \bar { C }$ and $A ^ { 2 } + B ^ { 2 } = C ^ { 2 }$. Which of the following statements, is correct?
  1. A $\bar { A }$ is parallel to $\bar { B }$
  2. B $\bar { A }$ is anti-parallel to $\bar { B }$
  3. C $\bar { A }$ is perpendicular to $\bar { B }$
  4. D $\bar { A }$ and $\bar { B }$ are equal in magnitude
Show answer

Correct answer: C

13
There are N coplanar vectors each of magnitude V. Each vector is inclined to the preceding vector at angle $\frac { 2 \pi } { N }$. What is the magnitude of their resultant?
  1. A $\frac { V } { N }$
  2. B V
  3. C Zero
  4. D $\frac { N } { V }$
Show answer & explanation

Correct answer: C

Zero, since the combination forms a polygon of N side.
By adding all sides give resultant zero.
Therefore, option (C) is the correct answer.
14
Vector $\bar { A }$ is shown in figure. The angle made by $\bar { A }$ with positive X-axis is
Motion in a plane – NEET-17959
  1. A $30 ^ { \circ }$
  2. B $90 ^ { \circ }$
  3. C $150 ^ { \circ }$
  4. D $60 ^ { \circ }$
Show answer

Correct answer: C

15
A car travels 6 km towards north at an angle of $45 ^ { \circ }$ to the east and then travels distance of 4 km towards north at an angle $135 ^ { \circ }$ to east. How far is the point from the starting point? What angle does the straight linse joining its initial and final positions makes with the east?
  1. A $\sqrt { 50 } \mathrm {~km}$ and $\tan ^ { - 1 } ( 10 )$
  2. B 10 km and $\tan ^ { - 1 } ( \sqrt { 5 } )$
  3. C $\sqrt { 52 } \mathrm {~km}$ and $\tan ^ { - 1 } ( 5 )$
  4. D $\sqrt { 52 } \mathrm {~km}$ and $\tan ^ { - 1 } ( \sqrt { 5 } )$
Show answer & explanation

Correct answer: C

Motion in a plane – NEET-17991
16
The maximum and minimum resultants of two forces are in the ratio 4 : 3. The forces are in the ratio....
  1. A 7 : 1
  2. B 1 : 5
  3. C 4 : 7
  4. D 3 : 7
Show answer & explanation

Correct answer: A

Motion in a plane – NEET-17987
17
Two bullets are fired horizontally with different velocities from the same height. Which will reach the ground first?
  1. A Slower one
  2. B Faster one
  3. C Both will reach simultaneously
  4. D Cannot be predicted
Show answer

Correct answer: C

18
A boat takes 2 hr to travel 8 km and come back in still water. If velocity of water is 4 km/hr, the time taken for going upstream 8 km and coming back is:
  1. A 2 hr
  2. B 2 hr 40 min
  3. C 1 hr 20 min
  4. D 3 hr
Show answer & explanation

Correct answer: B

Total distance travel = 8 + 8 = 16 km in 2 hr in still water
$\therefore V_{b}=\frac{16}{2}=8 \mathrm{~km} / \mathrm{hr}$
Effective velocity of boat in upstream = V$_{b}$ – V$_{w}$ = 8 – 4 = 4 km/hr
∴ Time taken to travel upstream, v = $\frac{8}{4}$ = 2 hrs
Effective velocity downstream = 8 + 4 = 12 km/s
Time taken downstream = $\frac{8}{12}$ = 40 min
∴ Total Time = 2 hr 40 min.
Therefore, option (B) is the correct answer.
19
A projectile can have same range R for two angles of projection. If $t _ { 1 }$ and $t _ { 2 }$ are the times of flight in the two cases, then what is the product of two times of flight?
  1. A $t _ { 1 } t _ { 2 } \propto R ^ { 2 }$
  2. B $t _ { 1 } t _ { 2 } \propto R$
  3. C $t _ { 1 } t _ { 2 } \propto \frac { 1 } { R }$
  4. D $t _ { 1 } t _ { 2 } \propto \frac { 1 } { R ^ { 2 } }$
Show answer

Correct answer: B

20
If the equation for the displacement of a particle moving on a circular path is given by θ = 2t$^{3}$ + 0.5, where θ is in radians and t in seconds, then the angular velocity of the particle after 2 s from its start is;
  1. A 8 rad/s
  2. B 12 rad/s
  3. C 24 rad/s
  4. D 36 rad/s
Show answer

Correct answer: C

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