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Rain is falling vertically with a speed of \(35~\text{ms}^{-1}\)${\mathrm{}}^{}$. Winds starts blowing after sometime with a speed of \(12~\text{ms}^{-1}\)${\mathrm{}}^{}$ in east to west direction. At what angle should a boy waiting at a bus stop hold his umbrella?

1. | \(16^{\circ}\) with the vertical |

2. | \(15^{\circ}\) with the vertical |

3. | \(19^{\circ}\) with the vertical |

4. | \(19^{\circ}\) with the horizontal |

Subtopic: Â Relative Motion |

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A motorboat is racing towards the north at \(25\) km/h and the water current in that region is \(10\) km/h in the direction of \(60^\circ\) east of the south. The resultant velocity of the boat is:

1. | \(12\) km/h at \(23 . 4^\circ\) east of west |

2. | \(22\) km/h at \(23 . 4^\circ\) north of east |

3. | \(22\) km/h at \(23 . 4^\circ\) east of north |

4. | \(20\) km/h at \(23 . 4^\circ\) north of west |

Subtopic: Â Relative Motion |

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The position of a particle is given by;

\(\overrightarrow{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m $\stackrel{}{\mathrm{}}$

where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in meters. The magnitude and direction of \(\overrightarrow{v}(t)\) at \(t=1.0\) s are:

1. | \(4\) m/s, \(53^\circ\) with \(x\)-axis |

2. | \(4\) m/s, \(37^\circ\) with \(x\)-axis |

3. | \(5\) m/s, \(53^\circ\) with \(y\)-axis |

4. | \(5\) m/s, \(53^\circ\) with \(x\)-axis |

Subtopic: Â Speed & Velocity |

Â 67%

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A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i\) m/s and moves in the \(x\text-y\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0\hat j)~\text{m/s}^2\). What is the speed of the particle at the instant its \(x\text-\)coordinate is \(84\) m?

1. | \(36\) m/s | 2. | \(26\) m/s |

3. | \(1\) m/s | 4. | \(0\) m/s |

Subtopic: Â Uniformly Accelerated Motion |

Â 70%

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Rain is falling vertically with a speed of \(35\) m/s. A woman rides a bicycle with a speed of \(12\) m/s in the east-to-west direction. What is the direction in which she should hold her umbrella?

1. | in the vertical direction only. |

2. | \(19^\circ\) with vertical towards east. |

3. | \(19^\circ\) with vertical towards the west. |

4. | \(19^\circ\) with vertical towards the south. |

Subtopic: Â Relative Motion |

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Galileo, in his book **T****wo new sciences**, stated that for elevations that exceed or fall short of \(45^\circ\) by equal amounts, the ranges:

1. | are equal to each other. |

2. | are not equal to each other. |

3. | are sometimes equal and sometimes not equal to each other. |

4. | depends on the difference between the angles. |

Subtopic: Â Projectile Motion |

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A hiker stands on the edge of a cliff \(490~\mathrm{m}\) above the ground and throws a stone horizontally with an initial speed of \(15\) m/s. Neglecting air resistance, the time taken by the stone to reach the ground and the speed with which it hits the ground are, respectively: (Take \(g=9.8~\mathrm{m/s^2}\))

1. | \(10\) s and \(99\) m/s |

2. | \(10\) s and \(15\) m/s |

3. | \(5\) s and \(99\) m/s |

4. | \(5\) s and \(15\) m/s |

Subtopic: Â Projectile Motion |

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A cricket ball is thrown at a speed of \(28\) m/s in a direction \(30^\circ\) above the horizontal. The time taken by the ball to return to the same level is:

1. \(2.5\) s

2. \(2.9\) s

3. \(3.5\) s

4. \(3\) s

Subtopic: Â Projectile Motion |

Â 85%

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An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. What is the angular speed of the motion?

1. | \(0.62\) rad/s | 2. | \(0.06\) rad/s |

3. | \(4.40\) rad/s | 4. | \(0.44\) rad/s |

Subtopic: Â Circular Motion |

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An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. Is the acceleration vector a constant vector? What is its magnitude?

1. \(\text{yes},\) \(2.3~\text{cm/s}^2\)

2. \(\text{no},\) \(5.3~\text{cm/s}^2\)

3. \(\text{yes},\) \(5.3~\text{cm/s}^2\)

4. \(\text{no},\) \(2.3~\text{cm/s}^2\)

Subtopic: Â Circular Motion |

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