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

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.

Steve · Answer

how long does it take to fall 45m?

4.9t^2 = 45
t = 3.03 seconds

So, how fast do they have to be moving to cover the 15m in 3 sec? 5m/s

How fast is 5m/s in terms we can really relate to?

That's 100m in 20 sec. Great athletes cover 100m in about 10 seconds, so it's only half as fast as that.

How about from a standing start? The world record for a standing broad jump is 3.7 meters, with a takeoff speed of about 3.7 m/s.

So, it looks like it'll take a running start. 5 m/s is 1km in 3.3 minutes. Not a sprint, but a good running speed.