6. Cleo and Clare are looking from their balcony to a swimming pool below that is located 15 m horizontally from the bottom of their building. They estimate the balcony is 45 m high and wonder how fast they would have to jump horizontally to succeed in reaching the pool. What calculations would you show to help them determine the answer? Evaluate the practicality of their being able to succeed at jumping into the pool.

Question

6. Cleo and Clare are looking from their balcony to a swimming pool below that is located 15 m horizontally from the bottom of their building.  They estimate the balcony is 45 m high and wonder how fast they would have to jump horizontally to succeed in reaching the pool.  What calculations would you show to help them determine the answer?  Evaluate the practicality of their being able to succeed at jumping into the pool.

jack1 · Answer

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jack1 · Answer

g = 9.8 m/s^2
s = ut + 1/2 a t^2

$\large s = ut + \frac12 a t^2$
where u = 0
a = g = 9.8
t = ?
s = 45
solve for t

jack1 · Answer

$\large s = ut + \frac12 a t^2$

$\large 45 = 0 + \frac12 g t^2$

$\large 45 = 4.9 t^2$

$\large 9.184 =  t^2$

t = 3.03 seconds from balcony to splat

jack1 · Answer

so, to safely make it into the pool, cleo/clare need to travel 16 m in 3.03 seconds
= horizontal speed of 5.28 m/s

thats a jog, not a sprint, so plenty safe

jack1 · Answer

the entry speed into the water is a bit fast tho...
3.03 x 9.8 roughly = 30m/s = 107 kms/hr into the water.. so probably like landing on concrete at that speed

mrnood · Answer

BEWARE!!!

Even professional cliff divers are diving from a height of approx. 30m

45m is WAY too high for anyone ot safely attempt to jump from it!

jack1 · Answer

maybe if they jumped with some rocks... to break the surface tension... then it'd be ok

mrnood · Answer

@Jack1 surface tension is NOT relevant to this question - it acts as a surface force, horizontally only. Rocks will not help

The key point here is that the body moving through water has massive 'drag' due to the density of the water compared to air. Therefore the acceleration upon hitting the water is extremely high and is liable to cause internal injuries from the 'shock'.

mrnood · Answer

If we model the body jumping as a cylinder with cross section of say 400mm diameter

the initial force from entering the water is 

I/2 rho v^2 A  (rho = density = 1000kg/m^3)

= 500 * 30^2 *pi * 0.2^2

54kN

If it a big jumper of mass 100kg then the acceleration = 54000/100 = 540 m/s^2

i.e. 50g

Bodies cannot normally withstand this type of acceleration without injury.

jack1 · Answer

@MrNood incorrect, breaking the surface tension allows for greater entry speed and creates micro-currents travelling in the same direction as the diver, allowing for a slower de-acceleration

mrnood · Answer

it is a totally insignificant effect compared to the drag force

mrnood · Answer

and in any case - the gross movement of the water caused by the rock is not related to surface tension - it simply reduces the effective velocity of entry.

Surface tension is a horizontal 'skin' effect and has no relevance to a body breaking into the fluid in macro scale

jack1 · Answer

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