All STD 11 - Motion in plane questions
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- 101. Ship \(A\) is sailing towards north -east with velocity \(\vec v = 30\,\hat i + 50\hat j\,km/hr\) where \(\hat i\) points east and \(\hat j\) , north. Ship \(B\) is at a distance of \(80\, km\) east and \(150\, km\) north of Ship \(A\) and is sailing towards west at \(10\, km/hr\). \(A\) will be at minimum distance from \(B\) is.........\(hrs\) 2019 Hard
- 102. The position vector of a particle changes with time according to the relation \(\vec r\left( t \right) = 15{t^2}\hat i + \left( {4 - 20{t^2}} \right)\hat j\). What is the magnitude of the acceleration at \(t = 1\) ? 2019 Medium
- 103. The stream of a river is flowing with a speed of \(2\,km/h.\) A swimmer can swim at a speed of \(4\,km/h.\) ....... \(^o\) should be the direction of the swimmer with respect to the flow of the river to cross the river straight . 2019 Medium
- 104. The trajectory of a projectile near the surface of the earth is given as\( y = 2x -9x^2\). If it were launched at an angle \(\theta_0\) with speed \(v_0\) then \((g = 10\, ms^{-2}\)) 2019 Hard
- 105. Two guns \(A\) and \(B\) can fire bullets at speed \(1\, km/s\) and \(2\, km/s\) respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is 2019 Medium
- 106. Two particles are projected from the same point with the same speed \(u\) such that they have the same range \(R\), but different maximum heights, \(h_1\) and \(h_2\). Which of the following is correct ? 2019 Hard
- 107. A conical pendulum of length \(1\,m\) makes an angle \(\theta \, = 45^o\) w.r.t. \(Z-\) axis and moves in a circle in the \(XY\) plane.The radius of the circle is \(0.4\, m\) and its centre is vertically below \(O\). The speed of the pendulum, in its circular path, will be ..... \(m/s\) (Take \(g\, = 10\, ms^{-2}\))
2017 Hard - 108. A ball of mass \(160\, g\) is thrown up at an angle of \(60^o\) to the horizontal at a speed of \(10\, m\,s^{-1}\) . The angular momentum of the ball at the highest point of the trajectcry with respect to the point from which the ball is thrown is nearly ........ \(kg\, m^2/s\) \((g\, = 10\, m\,s^{-2})\) 2014 Hard
- 109. A particle is released on a vertical smooth semicircular track from point \(X\) so that \(OX\) makes angle \(\theta \) from the vertical ( see figure). The normal reaction of the track on the particle vanishes at point \(Y\) where \(OY\) makes angle \(\phi \) with the horizontal. Then
2014 Hard - 110. The initial speed of a bullet fired from a rifle is \(630\, m/s\). The rifle is fired at the centre of a target \(700\, m\) away at the same level as the target. How far above the center of the target (in \(m\)) the rifle must be aimed in order to hit the target? (Take \(g=10 \;m/s^2\)) 2014 Hard
- 111. The position of a projectile launched from the origin at \(t = 0\) is given by \(\vec r = \left( {40\hat i + 50\hat j} \right)\,m\) at \(t = 2\,s\). If the projectile was launched at an angle \(\theta\) from the horizontal, then \(\theta\) is (take \(g = 10\, ms^{-2}\)) 2014 Hard
- 112. A ball projected from ground at an angle of \(45^o\) just clears a wall in front. If point of projection is \(4\,m\) from the foot of wall and ball strikes the ground at a distance of \(6\,m\) on the other side of the wall, the height of the walI is ........ \( m\) 2013 Hard
- 113. A projectile is given an initial velocity of \((\hat i + 2\hat j)\ ms^{-1}\), where \(\hat i\) is along the ground and \(\hat j\) is along the vertical. If \(g = 10\ m/s^2\) , the equation of its trajectory is 2013 Medium
- 114. The maximum range of a bullet fired from a toy pistol mounted on a car at rest is \(R_0= 10\, m\). What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity \(v = 20\, m/s\), on a horizontal surface ......... \(^o.\) \((g = 10\, m/s^2)\) 2013 Hard
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