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A particle is thrown with a speed u at a...

A particle is thrown with a speed `u` at an angle `theta` with horizontal. After how much time the velocity of particle will be perpendicular to the initial motion of direction

Text Solution

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The correct Answer is:
4
Initial velocity
` u = u cos theta hat(i) + u sin theta hat (j)`
Velocity after time t is
`u = u cos theta hat (i) + ( u sin theta - g t ) hat(j)`
Since u and v are perpendicular to each other therefore,
` vec (u) . vec (v) = 0 `
` ( u cos theta hat (i) + u sin theta hat(j) ) . [ u cos theta hat (i) + ( u sin theta - g t ) hat(j) ] = 0 `
` u^(2) cos ^(2) theta + u^(2) sin ^(2) theta - u sin theta g t = 0 `
` t = (u)/( g sin theta ) = (20)/( 10 xx (1)/(2)) = 4 s `
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