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A police van moving on a highway with a speedof 30 km h-' fires a bullet at a thief's carspeeding away in the same direction with aspeed of 192 km h-!. If the muzzle speed of thebullet is 150 m sl, with what speed does thebullet hit the thief's car ?(a) 95 m s' (b) 105 m s'(c) 115 m s (d) 125 m s! |
Answer» (C) 105 m s^-1Given: Speed of the police van vp = 30 KM h^-1 Converting into m/sec: = 30 x 1000 / 3600 = 25/3 ms^-1 Speed of the thief's car vt = 192 x 5/18 ms^-1 = 160/3 ms^-1 Formula we have to use here to CALCULATE the speed of the bullet: = Speed of police van + speed with which the bullet was actually fired Calculating the Speed of the bullet by USING the formula: = 25/3 + 150 = 475 / 3 ms^-1 Calculating the relative velocity of thief's car with respect to bullet: vbt = vb - vt Substituting the values into this formula we get: Vbt = (475/3 - 160/3) Vbt = 315/3 Vbt = 105 ms^-1 Therefore the speed at which the bullet hits the thief's car is 105 ms^-1. Option (C) 105 m s^-1 is the correct ANSWER. |
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