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.

Answer 1

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.

Answer 2

To determine the speed Cleo and Clare would have to jump horizontally to reach the pool, we can use principles of projectile motion.

First, let's define the variables:
- Horizontal distance from the bottom of the building to the pool: d = 15 m
- Height of the balcony: h = 45 m
- Acceleration due to gravity: g = 9.8 m/s^2

We need to find the required horizontal velocity (v) for Cleo and Clare to reach the pool.

The time it takes for Cleo and Clare to reach the pool can be calculated using the equation for vertical displacement in projectile motion: h = (1/2) * g * t^2.

Simplifying this equation, we get: t = sqrt((2 * h) / g).

To find the horizontal velocity, we can use the equation: d = v * t.

Rearranging this equation to solve for v, we get: v = d / t.

Now, let's substitute the given values into the equations:
- h = 45 m
- g = 9.8 m/s^2
- d = 15 m

Calculating the time taken in seconds using the formula: t = sqrt((2 * h) / g), we have:
t = sqrt((2 * 45) / 9.8)
t ≈ 3 seconds (rounded to two decimal places)

Now, we can calculate the required horizontal velocity using the formula: v = d / t.
v = 15 / 3
v = 5 m/s

Therefore, Cleo and Clare would have to jump horizontally with a speed of approximately 5 m/s to succeed in reaching the pool.

Now let's evaluate the practicality of their being able to succeed at jumping into the pool. This would depend on their physical capabilities.

Jumping with a horizontal speed of 5 m/s is not an achievable feat for most people. It would require a significant amount of strength, coordination, and athleticism. So, it is highly unlikely that Cleo and Clare would be able to successfully jump into the pool from their balcony. Attempting such a jump could also be dangerous and result in injuries. It would be much safer and more practical to use the conventional staircase or elevator to reach the pool.