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Question

An object is launched from a cliff 20 m above the ground at an angle of 30o above the horizontal with an initial speed of 30 m/s. How far does the object travel before landing on the ground? (in metre)

A
20
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B
203
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C
60
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D
603
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Solution

The correct option is D 603

Height of the cliff h1=20m

Velocity of projectile V=30m/s

Initial upward velocity vy=Vsinθ=30×sin30=15m/s.

Horizontal velocity, vx=Vcosθ=30cos30om/s

Time taken to reach maximum height, t1=Vyg=1510=1.5sec.

Height above the cliff h2=v2y2g=1522×10=11.25m

Therefore, the maximum height, hmax=h1+h2=20+11.25=31.25m.

Time taken to free fall from max height, t2=2hmaxg=2×31.25g=2.5sec.

Thus, the total time taken during the entire flight ttotal=t1+t2=1.5+2.5=4sec

Total horizontal distance covered R=vxttotal=30×cos30×4=603


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