Answer
Verified
439.8k+ views
Hint: Here, use the concepts of the velocity/speed that is distance travelled upon the time taken to solve this question. Since, the distance between the two persons remains the same, equate the two equations, take correlation between the two terms and find the required unknown distance.
Complete step by step answer:
Let “d” be the distance between the two persons.
Velocity of sound in steel pipe/metal is $v{}_m = 3630m{s^{ - 1}}$
Velocity of sound in metal is $v{}_A = 330m{s^{ - 1}}$
Time taken by the steel pipe is $t = {t_1}$
Time taken by the air $t = {t_2} = t + 0.5$
Now, velocity
$
\Rightarrow {v_m} = \dfrac{d}{{{t_1}}} \\
\Rightarrow d = {v_m} \times t{\text{ }}......{\text{(1)}} \\
$
$
\Rightarrow {v_A} = \dfrac{d}{{{t_2}}} \\
\Rightarrow d = {v_A} \times (t + 0.5){\text{ }}......{\text{(2)}} \\
$
Since, the left hand side of both the equations $(1){\text{ and (2)}}$ are the same, equate the right hand side of the equations.
$\Rightarrow {v_m} \times t = {v_A} \times (t + 0.5){\text{ }}$
Place the known values-
$
\Rightarrow 3630 \times t = 330 \times (t + 0.5) \\
\Rightarrow 3630t = 330t + 330(0.5) \\
\Rightarrow 3630t - 330t = 165 \\
\Rightarrow 3300t = 165 \\
\Rightarrow t = \dfrac{{165}}{{3300}} \\
\therefore t = 0.05s \\
$
Place the value of “t” in equation$(1)$
$
\Rightarrow d = {v_m} \times t{\text{ }} \\
\Rightarrow d = 3630 \times 0.05 \\
\therefore d = 181.5m \\
$
Therefore, the required answer – the distance between the two person is $181.5m$
Hence, from the given multiple choices – the option B is the correct answer.
Note: Always check the given units and the units asked in the solutions. All the quantities should have the same system of units. There are three types of the system of units.
-MKS System (Metre Kilogram Second)
-CGS System (Centimetre Gram Second)
-System International (SI)
Also, remember the conversional relations among the system of units to make all the given units in the same format.
Complete step by step answer:
Let “d” be the distance between the two persons.
Velocity of sound in steel pipe/metal is $v{}_m = 3630m{s^{ - 1}}$
Velocity of sound in metal is $v{}_A = 330m{s^{ - 1}}$
Time taken by the steel pipe is $t = {t_1}$
Time taken by the air $t = {t_2} = t + 0.5$
Now, velocity
$
\Rightarrow {v_m} = \dfrac{d}{{{t_1}}} \\
\Rightarrow d = {v_m} \times t{\text{ }}......{\text{(1)}} \\
$
$
\Rightarrow {v_A} = \dfrac{d}{{{t_2}}} \\
\Rightarrow d = {v_A} \times (t + 0.5){\text{ }}......{\text{(2)}} \\
$
Since, the left hand side of both the equations $(1){\text{ and (2)}}$ are the same, equate the right hand side of the equations.
$\Rightarrow {v_m} \times t = {v_A} \times (t + 0.5){\text{ }}$
Place the known values-
$
\Rightarrow 3630 \times t = 330 \times (t + 0.5) \\
\Rightarrow 3630t = 330t + 330(0.5) \\
\Rightarrow 3630t - 330t = 165 \\
\Rightarrow 3300t = 165 \\
\Rightarrow t = \dfrac{{165}}{{3300}} \\
\therefore t = 0.05s \\
$
Place the value of “t” in equation$(1)$
$
\Rightarrow d = {v_m} \times t{\text{ }} \\
\Rightarrow d = 3630 \times 0.05 \\
\therefore d = 181.5m \\
$
Therefore, the required answer – the distance between the two person is $181.5m$
Hence, from the given multiple choices – the option B is the correct answer.
Note: Always check the given units and the units asked in the solutions. All the quantities should have the same system of units. There are three types of the system of units.
-MKS System (Metre Kilogram Second)
-CGS System (Centimetre Gram Second)
-System International (SI)
Also, remember the conversional relations among the system of units to make all the given units in the same format.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE