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.

bobpursley · Answer

time to fall 45m
t=sqrt(2h/g)=sqrt(90/9.8) about three seconds...
velocity required=15m/3sec about=5m/sec = about 12 mph horizontally. Now the question how wide is the balcony and how much room do they have to accelerate to that velocity?

vf=sqrt(2ad)
5^2=2ad
ad=about 25m^2/s^2
Now "normal superhumans" can accelerate about 2.4 m/s^2, so she would need a distance of about
d=12.5/2.4= about six meters running distance. Few balconies offer that distance. If Clare is smart, she lets cleo try it first.