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Question

Two guns A and B can fire bullets at speeds 1kmsec-1 and 2kmsec-1 respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is :


A

1:2

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B

1:16

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C

1:8

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D

1:4

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Solution

The correct option is B

1:16


Explanation for correct option:

Option (b) 1:16

Step 1: Given data

Speed of bullet A: u1=1kmsec-1

Speed of bullet B: u2=2kmsec-1

Step 2: Formula used

We know that the formula for horizontal range is: R=u2sin2θg
The horizontal range for gun A,RmaxA=uA2g
The horizontal range for gun B,RmaxB=uB2g

Now, we know that:
Area, A=πR2
AR2

(Area)A(Area)B=RmaxA2RmaxB2=uA2uB22

To find the required answer, we will use the formula given below:

A1A2=u14u24

Here, A1 is the maximum range for gun A

A2 is the maximum range for gun B

u1 is the speed of bullet A

u2 is the speed of bullet B

Step 3: Find ratios of maximum areas covered by the bullets

By substituting the given values in the above-mentioned formula, we get:

A1A2=1424

A1A2=116

Thus, the ratio of maximum areas covered by the bullets fired by the two guns, on the ground is 1:16


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