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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 secLet 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=100sin30∘−gt ⇒−(vp)y=50−10t ⇒(vp)y=(10t−50) And applying equation of motion along x-axis, (vp)x=100cos30∘=50√3 and from figure, tan60∘=(vp)y(vp)x=10t−5050√3 ⇒√3=10t−5050√3 ⇒150=10t−50 ⇒10t=200 ∴t=20 sec Hence, the correct answer is option (d).

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