A particle is projected upwards with a velocity of 100 m/s at an angle of 60°, with the vertical.
Then time taken by the particle when it will move perpendicular to its initial direction. Please explain and give answer.

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Solution

Considering vertical motion we have:

(↑ +ve) u = 100cos60° => 100(1/2) = 50

a = -g = -10

When the velocity is perpendicular, the particle is going down and makes an angle of 30° with the vertical.

=> v = -100cos30° => -100√3/2...i.e. -50√3

so, using v = u + at we get:

-50√3 = 50 - 10t

=> 10t = 50 + 50√3

=> t = 5 + 5√3

or, t = 5(1 + √3) seconds.....about 13.7 seconds

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A particle is projected upwards with a velocity of 100 m/s at an angle of 60°, with the vertical. Then time taken by the particle when it will move perpendicular to its initial direction. Please explain and give answer.

A particle is projected upwards with a velocity of 100 m/s at an angle of 60°, with the vertical.
Then time taken by the particle when it will move perpendicular to its initial direction. Please explain and give answer.