Question

Someone HELP! WILL FAN AND MEDAL!!!!

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

@pooja195 @super123

Answer 2

@rvc

Answer 3

@peachpi @irishboy123

Answer 4

@SolomonZelman

Answer 5

@jagr2713 @Vocaloid @zepdrix @Mehek14 @ikram002p

Answer 6

@welshfella @imqwerty

Answer 7

Think about this problem in terms of time. If they drop VERTICALLY straight off the balcony, it will take some amount of time to reach the ground (which you can calculate using the acceleration due to gravity). However, their goal is to reach some distance HORIZONTALLY. The time they spend falling is limited by how long it takes to fall all the way vertically, so they had better push off the balcony with an initial horizontal velocity that's fast enough to cover the horizontal distance they want in the amount of time they have.

Now let's look at the math. Consider first the vertical movement. From the question, we have an initial velocity (vi) of 0 m/s, an acceleration (a) of 9.8 m/s^2, and a vertical distance (dy) of 45 m. We can use this information to calculate time (t) by using the following equation:

\[\Delta d_y=v_{i_y}t+\frac{1}{2}at^2\]\[45=(0)t+\frac{1}{2}(9.8)t^2\]\[t \approx3\]
This means that it will take approximately 3 seconds to fall 45 m vertically, meaning we also have 3 seconds to work with horizontally. The pool is 15 m away horizontally (dx), so we can calculate the horizontal speed (vx) required using the following equation:

\[v_x=\frac {\Delta d_x}{\Delta t}\]\[v_x={15 \over 3}\]\[v_x=5\]
This means a horizontal speed of about 5 m/s is required to reach the pool from the balcony. Whether this is practical is another story...5 m/s is fairly fast (about 11 mi/hr or 18 km/hr) and it's probably on the high end of the speeds even a decent runner is able to achieve.

Let me know if that makes sense!

Answer 8

Okay so we would need to add them together to get the end answer?

Answer 9

Add what together? All the information you need is in my answer above.

Answer 10

the 2 times? or would the highest one, 5m/s, be the answer? I'm sorry I'm tired lol

Answer 11

You are asked for two things, neither of which is a number (e.g. time, speed, etc):

1) What calculations would you show to help them determine the answer?
---> I've shown the calculations above

2) Evaluate the practicality of their being able to succeed at jumping into the pool.
---> See my final paragraph of the answer

Answer 12

Oooh, okay I see that now. Thank you so much! Could I message/mention you if I have anymore Physics trouble?

Answer 13

Sure tag me in any posts you need a hand with and if I'm around I'll try to have a look