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Q.

A ball is projected from the top of a tower with a velocity 3i^ + 4 j^ + 5 k^ ms-1 , where i^, j^ & k^are unit vectors along east, north and vertical upwards respectively. If the height of the tower is 30 m, its range is (g =10 ms-2 )

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a

12 m

b

9 m

c

15 m

d

25 m

answer is C.

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Detailed Solution

Horizontal component of the velocity of projection of the ball uh=32+42 m/s =5 m/s . Time of flight can be obtained from the equation 30 = -5T +12×10×T2 ⇒ T = 3 s Range R =uh×T =5×3 m = 15 m .

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A ball is projected from the top of a tower with a velocity 3i^ + 4 j^ + 5 k^ ms-1 , where i^, j^ & k^are unit vectors along east, north and vertical upwards respectively. If the height of the tower is 30 m, its range is (g =10 ms-2 )