JEE Physics - Motion in a Plane

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Question - 1

An aeroplane is to along straight line from A to B, and back again. The relative speed with respect to wind is V. The wind blows perpendicular to line AB with speed v. The distance between A and B is l. The total time for the round trip is_____

  • A \(\frac{2 \ell}{\sqrt{V^{2}-v^{2}}}\)
  • B \(\frac{2 v \ell}{V^{2}-v^{2}}\)
  • C \(\frac{2 V \ell}{V^{2}-v^{2}}\)
  • D \(\frac{2 \ell}{\sqrt{V^{2}+v^{2}}}\)

Question - 2

Passengers in the jet transport A flying east at a speed of 800 kmh-l observe a second jet plane B that passes under the transport in horizontal flight. Although the nose of B is pointed in the 45o north east direction, plane ,B appears to the passengers in,4 to be moving away from the transport at the 60o angle as shown. The true velocity of B is______

  • A 586 kmh-l 
  • B 400\(\sqrt{2}\)  kmh-l 
  • C 717 kmh-l 
  • D 400 kmh-l 

Question - 3

A sphere of radius l0 cm is in contact with a wedge as shown. The point of contact of the sphere is at height of 2 cm above the ground. If the wedge is moving leftwards with 20 cm/s, the sphere is moving with______

  • A 12 cm/s
  • B 15 cm/s
  • C 18 cm/s
  • D 21 cm/s

Question - 4

A2 m wide truck is moving with a uniform speed V0 = 8 m/s along a straight horizontal road. Apedestrain starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is_______

  • A 2.62 m/s
  • B 4.6 m/s
  • C 3.57 m/s
  • D 1.414 m/s

Question - 5

In figure the angle of inclination ofthe inclined plane is 30o. The horizontal velocity V0 so that the particle hits the inclined plane perpendicularly is________

  • A \(V_{0}=\sqrt{\frac{2 g H}{5}}\)
  • B \(V_{0}=\sqrt{\frac{2 g H}{7}}\)
  • C \(V_{0}=\sqrt{\frac{g H}{5}}\)
  • D \(V_{0}=\sqrt{\frac{g H}{7}}\)

Question - 6

A particle P is projected from a point on the surface of long smooth inclined plane and Q starts moving down the ptane from the same position. P and Q collide after 4 second. The speed of projection of p is ___ : (g = (10 m/s2)

  • A 5 m/s
  • B l0 m/s
  • C 15 m/s
  • D 20 m/s

Question - 7

The velocity of a particle moving in a positive direction of the x-axis varies as \(\nu=\alpha \sqrt{x}\) where \(\alpha\) is a positive constant. Assuming that at the moment t = 0, the particte was located at the point x = 0_____

  • A in the motion, the acceleration is constant
  • B velocity at any time will be \(\alpha\)/t
  • C vetocity at anytime will be \(\frac{\alpha^{2} t}{2}\) 
  • D mean velocity of particte averaged over the time that the particle takes to cover first s meter is \(\frac{\alpha \sqrt{s}}{2}\)

Question - 8

An aeroplane is flying horizontally with constant velocity vo at a height h from the ground. At an instant, it is vertically above a cannon (on the ground). At the same instant, a shell is fired to hlt the aeroplane withmuzzle speed u :______

  • A Angle of projection must be equal to \(\cos ^{-1}\left(\frac{v_{0}}{u}\right)\)
  • B Muzzle speed should not be less than \(\sqrt{v_{0}^{2}+2 g h}\)
  • C Angle of projection cannot be less than \(\cos ^{-1}\left(\frac{v_{0}}{\sqrt{v_{0}^{2}+2 g h}}\right)\)
  • D None of these

Question - 9

Two small balls A and B are launched in the same vertical plane simultaneously, with same speed of 20 m/s at t = 0.Ball A has an initial horizontal velocity and ball B has initial velocity at an angle \(\theta\) above the line joining A and.B as shown. If the projectiles collide in mid-air at time t, then______

  • A \(\theta=30^{\circ}\)
  • B \(\theta=60^{\circ}\)
  • C \(t=\frac{20}{\sqrt{3}} \mathrm{~s}\)
  • D \(t=\frac{10}{\sqrt{3}} \mathrm{~s}\)

Question - 10

Find the component of vector \(\overrightarrow{\mathbf{A}}=(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}})\) along the direction \((\hat{\mathbf{i}}-\hat{\mathbf{j}})\)

  • A \(-\frac{1}{2}(\hat{i}-\hat{j})\)
  • B \(-\frac{1}{2}(\hat{i}+\hat{j})\)
  • C \(\frac{1}{2}(\hat{i}-\hat{j})\)
  • D \(\frac{1}{2}(\hat{i}+\hat{j})\)
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