Need to find the distance but how?

[windrar]

Participants in a road race take water from
a refreshment station and throw their
empty cups away farther down the course.
If a runner has a forward speed of 6.20 m/s,
how far in advance of a garbage pail
should he release his water cup if the
vertical distance between the lid of the
garbage can and the runner’s point of
release is 0.50 m?

I am still in grade 11 so please make it simple for me. Thank you very much.

 

[TheWye]

well, I suppose the pictorial representation of the graph should be something like this. The green dots are the projection of the cup after it is released by the runner and x is that distance we want to find.

And I think the runner does not actually throw the cup, but just releases it and let it fall freely. Because if the runner does throw it, the question would have stated the speed of the throw.

Anyway, first thing is to consider how long it will take for the cup to reach the height of the lid of the garbage from the time when the runner releases the cup. To do this, we look at the equation of the free fall:

s = 1/2 g t²

where:
g is the gravitational acceleration,
s is the distance of the fall,
and t is the time taken to fall that distance

We already know s and g, so solving for t should be simple. In our case, s will be the 0.5 meters distance between the hand of the runner and the lid of the garbage. In my picture, it is the line colored in red.

Now that we have got the time taken to complete the 0.5 meters distance, we can now calculate how far from the garbage pail the runner should release the cup. So now the problem is quite simple.

Just look at it this way: the runner is running at the speed of 6.20 m/s and he needs to cover the distance x within the time t. For this, the only equation you need to use is the equation of speed :

x = v x t

So, since time t is already known from our previous calculation so solving for this will be very simple.

Hope this helps

 

[nlightner]

To find the distance, we can use the formula d = v*t, where d is distance, v is speed, and t is time. In this scenario, we want to find the distance at which the runner should release their water cup so that it lands in the garbage pail. We know the runner's forward speed (v = 6.20 m/s) and the vertical distance between the lid of the garbage can and the runner's point of release (d = 0.50 m).

To find the time (t), we can use the formula t = d/v, which rearranges to t = 0.50 m / 6.20 m/s = 0.08 seconds. This means that the runner should release their water cup 0.08 seconds before reaching the garbage pail in order for it to land in the pail.

If you need to find the distance in meters, we can use the formula d = v*t, which becomes d = 6.20 m/s * 0.08 seconds = 0.496 meters. Therefore, the runner should release their water cup 0.496 meters before reaching the garbage pail.

I hope this helps! Let me know if you have any further questions.