Calculating the height of a bridge

[iankirby]

Is it possible to calculate the height of a bridge by dropping stone into the river and timing it?

I have tried a couple of formulae, but seem to be way off mark.

I realise drag etc can affect the times, but how acuurate should it be?

[Dr Hungry]

You should be able to use the formula s = ut + 1/2 at^2

s being the height of the bridge

u being the initial velocity ( =0 ms-1)

t being the time you record

a being acceleration due to gravity ( = 9.81 ms-1 on Earth)

Acceleration might actually be a little less than this due to the affect of drag so you could get a slightly larger value than is true, but it shouldn't make that much of a difference.

[Dr Hungry]

Of course all that depends upon the accuracy of your timing!

Good luck!

[shaun_04]

so just use

height of bridge = 4.9 x time^2 (time squared)

this will give height in metres btw (assuming you have time in seconds obv)

[Mortartube]

Or dangle a piece of rope over the bridge until it just touches the water. Mark it and drag it in. Then measure it.

[JudgeJ]

As summarised by shaun_04, The elapsed time (squared) times 16 will give you the answer in feet. Elapsed time (squared) times 4.9 gives the answer in metres.

As Dr Hungry suggests, whilst his formula will give you the answer you seek, it will be very much dependant upon your ability to measure the elapsed time accurately. You would be very lucky to time it to within half a second. (It takes humans, at best, between 0.2 and 0.3 seconds to react to an event).

If the bridge is really16 feet (5m) high it will take exactly one second for your stone to hit the water. If you record this time as being between 0.75 and 1.25 seconds, your height calculation will be anywhere between 9 and 25 feet - up to 50% adrift. Increase the bridge�s height to 144 feet (stone takes 3 seconds) and the same quarter second inaccuracy will give you a height of between 121 and 159 feet.

A good idea theory, but on balance, I prefer Mortartube�s excellent idea!

[Catso]

In practical terms, I'd say you can't.

As others have said, you have to be very (impossibly) accurate with the timing. Due to the dynamics of it, a small timing error produces a larger error in the result.

[WaldoMcFroog]

Of course, if you film yourself with a digital camera dropping the stone and follow it until it hits the water, you could get the timing pretty more accurately using the playback!

[Catso]

Very neat idea Mr McFrog. Accurate to 1/25 second!