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Motion in a Plane · Question 19

AIPMT 2015 (Cancelled)MCQMedium📈 Topic in 0% papers+4−1
1

A ship A is moving Westwards with a speed of 10 km h-1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h-1. The time after which the distance between them becomes shortest, is

  1. 5 2 h
  2. 10 2 h
  3. 0 h
  4. 5 h

Answer

(4) 5 h

Solution

Take A at rest: velocity of B relative to A, vBA = vB - vA = 10 km/h North + 10 km/h East

⇒ | vBA| = 10 2 km h-1, at 45 to the line BA (North).

The distance is shortest when B reaches the foot of the perpendicular from A on its relative path.

Distance moved along the relative path = 100 45 = 50 2 km

∴ t = 50 210 2 = 5 h

Answer: (4)

AIPMT 2015 (Cancelled)

Keep practising — Motion in a Plane

2

A projectile is fired from the surface of the earth with a velocity of 5 m s-1 and angle with the horizontal. Another projectile fired from another planet with a velocity of 3 m s-1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in m s-2) is (Given g = 9.8 m s-2)

  1. 3.5
  2. 5.9
  3. 16.3
  4. 110.8
AIPMT 2014
3

A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s and (13 m, 14 m) at time t = 5 s. Average velocity vector ( vav) from t = 0 to t = 5 s is

  1. 15 (13 i + 14 j )
  2. 73 ( i + j )
  3. 2 ( i + j )
  4. 115 ( i + j )
AIPMT 2014
4

The velocity of a projectile at the initial point A is (2 i + 3 j) m/s. Its velocity (in m/s) at point B is [figure]

  1. 2 i - 3 j
  2. 2 i + 3 j
  3. -2 i - 3 j
  4. -2 i + 3 j
NEET 2013
5

Vectors A, B and C are such that A B = 0 and A C = 0. Then the vector parallel to A is

  1. A B
  2. B + C
  3. B C
  4. B and C
NEET 2013 (Karnataka)
6

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

  1. = -1 ( 14 )
  2. = -1(4)
  3. = -1(2)
  4. = 45
AIPMT 2012 (Prelims)
7

A particle has initial velocity (2 i + 3 j ) and acceleration (0.3 i + 0.2 j ). The magnitude of velocity after 10 seconds will be

  1. 9 2 units
  2. 5 2 units
  3. 5 units
  4. 9 units
AIPMT 2012 (Prelims)
8

A projectile is fired at an angle of 45 with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is

  1. 45
  2. 60
  3. -1 ( 12 )
  4. -1 ( 32 )
AIPMT 2011 (Mains)
9

A particle moves in a circle of radius 5 cm with constant speed and time period 0.2 s. The acceleration of the particle is

  1. 15 m/s2
  2. 25 m/s2
  3. 36 m/s2
  4. 5 m/s2
AIPMT 2011 (Prelims)
10

A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10 m/s2, the range of the missile is

  1. 40 m
  2. 50 m
  3. 60 m
  4. 20 m
AIPMT 2011 (Prelims)
11

A body is moving with velocity 30 m/s towards east. After 10 seconds its velocity becomes 40 m/s towards north. The average acceleration of the body is

  1. 1 m/s2
  2. 7 m/s2
  3. 7 m/s2
  4. 5 m/s2
AIPMT 2011 (Prelims)

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