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Height and Distance

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1.  Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is: A. 173 m B. 200 m C. 273 m D. 300 m Answer:  Option  C Explanation: Let AB be the lighthouse and C and D be the positions of the ships. Then, AB = 100 m,  ACB = 30° and  ADB = 45°. AB = tan 30° = 1           AC = AB x  3  = 100 3  m. AC 3 AB = tan 45° = 1           AD = AB = 100 m. AD  CD = (AC + AD) = (100 3  + 100) m = 100( 3  + 1) = (100 x 2.73) m = 273 m.
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Logic

when a man moves in the direction of train, the train speed is decreased by his own speed. If he moves in the opposite directon he finds the train speed to be much greater. So when is moving in the same direction his speed must be subtracted from that of train speed. If he moves in the opposite direction to that of train, then his speed must be added to the train speed. moving in same directon: SUBTRACT moving in opposite directon: ADD
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Train Problem

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1.  A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? [A]. 120 metres [B]. 180 metres [C]. 324 metres [D]. 150 metres Answer : D Expalanation: Speed= 60 x 5 m/sec = 50 m/sec. 18 3 Length of the train = (Speed x Time).  Length of the train = 50 x 9 m = 150 m. 3 Important formula: Distance = Speed*Time. Time = Distance/Speed. Speed= Distance/Time. distance is also known as length First we have to change the speed to seconds Let me explain about converting km/hr into m/s in detail. 1 km = 1000 meters. 1 hr = 3600 seconds. 1 km/hr = 1000/3600 m/s = 10/36 m/s = 5/18 m/s. Therefore 1 km/hr = 5/18 m/sec. Similarly 60 km/hr = 60 x 5/18 m/sec. why should I convert it from km/hr to m/sec? Because, the time taken by the train is given in terms of seconds (9 seconds) and the 4 options are in terms of metres. But the speed of the train is given in terms of km/hr. So
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