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Question

# A train is moving with a constant speed of 10 m/s in a circle of radius 16π m. The plane of the circle lies in horizontal. x-y plane. At time t=0, train is at point P(16π,0,0) and moving in counter-clockwise direction. At this instant a stone is thrown from the train with speed 10 m/s relative to train towards negative x-axis at an angle of 37∘ with vertical z-axis. Find the velocity of particle relative to train at the highest point of its trajectory.

A
(3^i+4^j)ms1
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B
(3^i+5^j)ms1
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C
(6^i+8^j)ms1
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D
(4^i+10^j)ms1
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Solution

## The correct option is B (4^i+10^j)ms−1The stone has three components of velocity.The velocity of stone vs=vs/train+vtrainvs/train=−10cos37∘^i+10sin37∘^km/s ;vtrain=10^jvs=−10cos37∘^i+10^j+10sin37∘^km/s→vs=−6^i+10^j+8^kAt the highest point of projectile the vertical velocity will be zeroVelocity along z-direction is 8m/s, thus, time to reach max height isT=vzg=810=0.8sVelocities along x and y directions won't change as there is no aceleretion in these directions.At max height velocity of the particle is→vs=−6^i+10^jTill this instant distance travelled by the train is =10×0.8=8m8R=816π=π2⇒ angular displacement of the train is 900→vt=−10^i→vp/t=→vs−→vt=4^i+10^j

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