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A bowler throws a cricket ball at a speed of \[120\dfrac{{Km}}{h}\] . How long does this ball take a distance of $20$ meters to reach the batsman?

seo-qna
Last updated date: 21st Jul 2024
Total views: 348.3k
Views today: 8.48k
Answer
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Hint: First we need to convert the given units into our required units. Since the unit of time is second(s), we need to convert hours into seconds and also we have to convert kilometers into meters.
We all know that,
$1$Kilometer$ = $$1000$meter
(i.e.) $1$km$ = $$1000$m
$1$hour$ = $$3600$second
(i.e.) $1$h$ = $$3600$s
Here our question is to calculate the time taken for a distance of $20$ meters to reach the batsman.

Formula used:
\[Speed = \dfrac{{Distance}}{{Time}}\]
Since our question is to calculate the time taken, we need to change the above formula as follows.
$Time = \dfrac{{Distance}}{{Speed}}$

Complete step-by-step solution:
It is understood from the question that the values of speed and distance are given.
That is, it is given that speed$ = $\[120\dfrac{{Km}}{h}\]
Distance$ = $$20m$
Here our question is to calculate the time taken for a distance of $20$ meters to reach the batsman.
We all know that, $1$ Kilometer$ = $$1000$meter
(i.e.) $1$km$ = $$1000$m
$1$ hour $ = $$3600$second
(i.e.) $1$h$ = $$3600$s
Hence, speed$ = $\[120 \times \dfrac{{1000m}}{{3600s}}\]
When cancelling the numbers, we get
That is, speed$ = $\[\dfrac{{100}}{3}m{s^{ - 1}}\]
Now apply the obtained values in the formula.
$Time = \dfrac{{Distance}}{{Speed}}$
Distance$ = $$20m$
Speed$ = $\[\dfrac{{100}}{3}m{s^{ - 1}}\]
Hence,
\[Time = \dfrac{{20m}}{{\dfrac{{100m}}{{3s}}}}\]
Taking reciprocals, we have
\[Time = 20m \times \dfrac{{3s}}{{100m}}\]
On cancelling, we get
$Time = \dfrac{{60}}{{100}}s$
Now, convert it into decimal form.
$Time = 0.6s$ is the required answer.
That is, the ball takes $0.6$ second to reach the batsman.

Note: First we need to convert the given units into our required units. Suppose we are asked to calculate the distance, we just convert the formula for our convenience.
That is,
\[Speed = \dfrac{{Distance}}{{Time}}\]into
\[Speed \times Time = Dis\tan ce\]
The SI unit of speed is$m{s^{ - 1}}$ .
The SI unit of time is$s$ .
The SI unit of distance is$m$ .