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.
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.
To determine the speed at which Cleo and Clare would need to jump horizontally to reach the pool, we can use basic kinematic equations. Let's denote the horizontal distance to the pool as x and the height of the balcony as h.
First, we need to find the time it would take for them to fall from the height of the balcony to the pool. We can start by using the equation for vertical displacement under free fall:
h = (1/2)gt^2
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time in seconds.
Rearranging the equation, we get:
t = √(2h/g)
Plugging in the values, we have:
t = √(2 * 45 m / 9.8 m/s^2) ≈ 3.02 seconds
Next, we can calculate the horizontal distance:
x = velocity * time
The velocity needed will allow them to cover the horizontal distance x in the time t. Rearranging the equation, we get:
velocity = x / t
Plugging in the values, we have:
velocity = 15 m / 3.02 s ≈ 4.97 m/s
So, Cleo and Clare would need to jump horizontally at a speed of approximately 4.97 m/s to reach the pool.
Now, let's evaluate the practicality of their ability to succeed in jumping into the pool.
The average long jump distance for professional athletes is around 8.95 meters for men and 7.52 meters for women. Considering the horizontal distance required is only 15 meters, it is highly unlikely for an average person to achieve such a jump from a standing position.
Additionally, attempting a jump of this magnitude could pose serious risks, including injury. Most people have limited jumping abilities, and trying to cover such a large horizontal distance could result in falls, fractures, or other accidents.
In conclusion, it is not practically feasible for Cleo and Clare or the average person to succeed in jumping into the pool from their balcony.