Concept explainers
A shell fired at a target 800 m away was heard by someone standing near the gun to strike the target 5.0 s after leaving the gun. Compute the average horizontal velocity of the shell. The air temperature is 20 °C.
The average speed of the shell fired at a target which is
Answer to Problem 28SP
Solution:
Explanation of Solution
Given data:
Distance of the target from the observer is
Temperature of the air is
Observer hears the sound of the shell striking the target
Formula used:
The relation between temperature and speed of sound is,
Here,
The speed of sound at
The formula for distance is
Here,
Explanation:
Calculate the time that the sound takes to reach the observer from the target when shell hits it.
Recall the formula for unit conversion of temperature.
Convert the unit of temperature at
Substitute
Convert the unit of temperature at
Substitute
Recall the formula for the speed of sound in terms of temperature,
Rearrange the equation for
Substitute
Recall the formula for the distance travelled.
Rearrange the equation for
Substitute
Since the observer hears the sound of shell striking the target
Here,
Substitute
Now, calculate the speed of the shell.
Recall the formula for the distance travelled.
Here,
Rearrange the equation for
Substitute
Conclusion:
The speed of the shell is
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