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)
Originally posted by Audi: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.