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Question

The maximum horizontal range is obtained when _________.


A

θ=45°

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B

θ=30°

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C

θ=90°

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D

θ=180°

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Solution

The correct option is A

θ=45°


Step 1: Write the equation and define the variables in the equation.

We know, horizontal range is given by the equation, R=v02sin2θg

where,

Rhorizontalrange

v0initialvelocity

θangleofprojection

gaccelerationduetogravity

Since v02g is constant for all the given angles, the range is maximum when sin2θ is maximum.

Step 2: Explanation for correct option:

In case of Option A

when θ=45°, sin2θ=sin90°=1

sin2θ is maximum when 2θ is 90°

i.e., when θ=45°

Option A, θ=45° is the correct answer.

Step 3: Explanation for incorrect options:

In case of Option B

when θ=30°, sin2θ=sin60°=32

Option B is incorrect because 1>32 sin(2×45°)>sin(2×30°)

Option B is incorrect

In case of Option C

when θ=90°, sin2θ=sin180°=0

Option C is incorrect because 1>0 sin(2×45°)>sin(2×90°)

Option C is incorrect

In case of Option D

when θ=180°, sin2θ=sin360°=0

Option D is incorrect because 1>0 sin(2×45°)>sin(2×180°)

Hence, correct option is (A).


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