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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.Open in App

Solution

The correct option is **B** (4^i+10^j)ms−1

The stone has three components of velocity.

The stone has three components of velocity.

The velocity of stone vs=vs/train+vtrain

vs/train=−10cos37∘^i+10sin37∘^km/s ;vtrain=10^j

vs=−10cos37∘^i+10^j+10sin37∘^km/s

vs/train=−10cos37∘^i+10sin37∘^km/s ;vtrain=10^j

vs=−10cos37∘^i+10^j+10sin37∘^km/s

→vs=−6^i+10^j+8^k

At the highest point of projectile the vertical velocity will be zero

At the highest point of projectile the vertical velocity will be zero

Velocity along z-direction is 8m/s, thus, time to reach max height is

T=vzg=810=0.8s

Velocities 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^j

Till this instant distance travelled by the train is =10×0.8=8m

8R=816π=π2⇒ angular displacement of the train is 900

→vt=−10^i→vp/t=→vs−→vt=4^i+10^j

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