Question

There is a rock that is 10 feet tall, with a three foot ledge at the bottom. Beyond the three foot ledge is water. How fast would one half to run to clear the ledge?

Answer 1

@matt101

Answer 2

To clear the rock, the horizontal velocity has to be high enough that a person travels the length of the ledge before reaching the ground.

In other words, calculate first the time it takes to reach the ground from a rock 10 feet tall. Then, use that time, along with the distance that needs to be traveled to clear the ledge (3 feet) to calculate horizontal speed!

Answer 3

It takes about a third of a second for her to reach the ledge if we assume that she just walks right off the rock. So, how would I use that to calculate horizontal speed?

Answer 4

Can I see your calculation?

Answer 5

I did something wrong, it would be more than a third of a second. I converted 10 feet to meters, and then .098 being 1%s worth of movement in a second, I divided 3.048(10 ft converted) by that to get ~31.1. Which I am pretty sure I am not allowed to do :s

Answer 6

It's ok to convert to meters (that's what I did). However, you can't do anything with 1s worth of movement, because we don't know that it takes 1 s to fall - it's that time that we're trying to find!

The question gives us or we know distance (3.048 m), initial speed (0 m/s), acceleration (9.8 m/s^2). Given d, vi, and a, the equation that will let us solve for t is this one:

\[d=v_i t+\frac{1}{2}at^2\]
When you plug the appropriate values into this equation, what do you get for t?

Answer 7

I got t=.7886

Answer 8

Me too. So that's the maximum time we have to travel horizontally as well. Using this time, we need to travel 0.9144 m (3 feet) horizontally to clear the ledge. We have distance and time, so what is the speed?

Answer 9

1.1595 m/s

Answer 10

That's it!

Answer 11

So that is the minimum velocity someone would have to have to clear the ledge?

Answer 12

Yes

Answer 13

That makes a lot of sense. Thanks!