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Question: The ceiling of a tunnel is of 5m high. What is the maximum horizontal distance that a ball thrown wi...

The ceiling of a tunnel is of 5m high. What is the maximum horizontal distance that a ball thrown with a speed of 20 m/s, can go without hitting the ceiling of the tunnel ? (Take g = 10 m/s2)

A

30 m

B

40 m

C

30230\sqrt{2}m

D

20320\sqrt{3}m

Answer

20320\sqrt{3}m

Explanation

Solution

Q u2sin⁡2θ2g\frac { u ^ { 2 } \sin ^ { 2 } \theta } { 2 g } = 5 m

̃ (20)2sin⁡2θ20\frac { ( 20 ) ^ { 2 } \sin ^ { 2 } \theta } { 20 } = 5

̃ sin q = 12\frac { 1 } { 2 } ̃ q = 30º

R = u2sin⁡2θg\frac { u ^ { 2 } \sin 2 \theta } { g } = (20)2sin⁡60∘10\frac { ( 20 ) ^ { 2 } \sin 60 ^ { \circ } } { 10 } = 20 3\sqrt { 3 }