The Running Race

Launch worksheet

Launch solution 

Track and Field Course

Sihasak Prachum / 123rf.com.

You’re training one of the fastest athletes on the planet and it is your job to make sure they reach their new goal; run a 500m sprint in under 60 seconds. If they complete it, it will bring the team the confidence they need heading into the Olympics.

You wait at the finish line, waiting for someone to shoot the starting gun at start line of the 500m (it’s a 500 m long straight track). The world record sitting at 57.69 seconds, you wonder if this will be the day they break the record. BANG. You start the timer when you hear the gun shot.

And before you could blink it was over. You stop the timer as they cross the finish line in front of you and look down at the timer to see 61.39s, not fast enough. You tell your runner to take a break and try again, all up they do 4 runs and record the times: 61.39s, 62.3s, 59.1s and 60.9s.

To then find their average time, you average the 4 values:

Average time = (sum of shot durations) / number of readings

Average time = (61.39 + 62.3 + 59.1 + 60.9) / 4

Average time = (243.69) / 4

Average time = 60.92 seconds

But wait, if you started the time after hearing the gunshot sound from the start of the 500m track, then it would have taken time for the sound to actually get to you. The speed of sound is 343 m/s; you can use this to work out how much time you missed out:

range = time delay × speed

sound delay = range / speed

sound delay = 500 m / (343 m/s)

sound delay = 1.45s

actual time = average time + sound delay

actual time = 60.92s + 1.45s

actual time = 62.37s

After taking into account the time for the sound of the gunshot to reach you, it turns that they haven’t broken the magical sixty second mark. You tell them to train harder: they’ll need to work hard for the Olympics!

Real Life Example – Lightning

41789107 - beautiful view of dramatic stormy sky and lightning over nha trang bay of south china sea in khanh hoa province at night in vietnam. nha trang city is a popular tourist destination of asia.

Efired / 123rf.com.

You may have already done this when you were younger, but you can measure how far away a lightning bolt is by counting the number of seconds between when you see it and when you hear it.

When you see the lightning bolt, start counting. Then multiply that number by 340 and that’s the approximate distance that the lightning bolt was from you.

Let’s pretend that your little sister or brother is scared out because there is a storm. You see a lightning bolt and count the number of seconds before you hear it. You count… 9 seconds.

range = time delay × speed

range = 9 × 340 m/s

range = 3060 m

You can reassure your little brother or sister that there is no need to panic, that lightning strike was 3 km away.

(NOTE: Storms can be spread over large areas and just because that lightning bolt wasn’t nearby doesn’t mean none will be.  Even math can’t save you once the lightning storm is closer to you and being struck by lightning is not on the to-do list. Stay safe during large storms and avoid going outside).