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Question

A particle is projected upwards with a velocity of 100 m/sec at an angle of 60 with the vertical. Find the time when the particle will move perpendicular to its initial direction taking g=10 m/sec2.

A
2 sec
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B
4 sec
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C
10 sec
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D
20 sec
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Solution

The correct option is D 20 sec
Let say at point P velocity of particle makes 90 with initial velocity (u=100 m/s as shown in the figure below.


Let us consider, it takes t sec to reach the point P.


Applying the equation of motion along y-axis,

(vp)y=100sin30gt

(vp)y=5010t

(vp)y=(10t50)

And applying equation of motion along x-axis,

(vp)x=100cos30=503

and from figure,

tan60=(vp)y(vp)x=10t50503

3=10t50503

150=10t50

10t=200

t=20 sec

Hence, the correct answer is option (d).

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