In a recent Olympic diving event, a male participant stood on a
platform and performed a dive into the water. During the dive, the
horizontal distance of the participant away from the platform x m,
and the corresponding vertical distance of the participant above
the platform, y m, are related by the equation
y = 13/10 x -x^2/2
x
0
1
2 3
4
5 6
y
0 0.8
0.6 -0.6
-2.8
-6 -10.2
For both axes, use 2cm :1unit
By drawing a tangent, find the gradient of the curve at the
point (3,-0.6). What can be said about the movement of the
participant at this instant?
My gradient is -1.69. Not sure what gradient represents. Funny,
it's a distance over a distances (y/x), usually it will be a
distance/ time or something like that and we can deduce the meaning
easily. Well, my illogical answer is the rate of decrease of the
man's height.
Next, I am asked
Is the graph useful in finding the position of the participant
beyond a horizontal distnace of 4.4m, given that he enetered the
water when he was 4.4m away from the platform. Justify your
answer.
I say Yes. From the graph, we know that as the participant swims
away and the horizontal dist. increases, the vertical distance also
increases (i mean, become more -ve). THis tells us the diver is
going deeper and deeper into the water. (he's a diver ya see, so
should be swimming towards the bottom of the sea)
Hi Audi,
I am sorry as I cannot give you any guarantee that my answers
are correct, but for the first question, since they asked about the
movement of the participant, maybe you could answer that the diver
is going downwards into the water at an angle of 59.4 degree.
Your 2nd answer is generally correct, though you should remove
the part on diving into the sea. Since it is an Olympic diving
competition, they will be using a 10~15m deep swimming pool.