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Question

# A body is projected from the top of a tower of height 32 m with a velocity of 20 m/s at an angle of 37∘ above the horizontal. The time of flight of the projectile is (Take g=10 m/s2)

A
85 s
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B
2 s
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C
8 s
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D
4 s
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Solution

## The correct option is D 4 sTime of flight only depends on the vertical component of velocity. Initial vertical velocity uy=20sin37∘=20×35=12 m/s (taking upward direction as positive) Displacement of the body when it reaches the ground h=−32 m Using the second equation of motion, h=uyt−12gt2 ⇒−32=12t−5t2 ⇒5t2−12t−32=0 ⇒5t2−20t+8t−32=0 ⇒5t(t−4)+8(t−4)=0 ⇒(5t+8)(t−4)=0 ⇒t=4 (since time cannot be negative) Hence the time of flight is 4 s.

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