How Does the Height of a Parachute Change with Horizontal Displacement?

In summary, the height h(x) of a parachute above the ground varies with the horizontal displacement x from a landing target as h(x) = 50sin^-1 (0.1x). The rate of change of h with respect to x at x = 6m can be found by taking the derivative of h(x) which is 1 / sqrt(1-x^2). This is equivalent to d/dx( sin^-1 (0.1x)) = 1 / sqrt(1-x^2).
  • #1
JakePearson
52
0
the height h(x) in meters above the ground of a parachute varies with her horizontal distplacement x in meters from a landing target on the ground as h(x) = 50sin^-1 (0.1x). what is the rate of change of h with respect to x at x = 6m?

i was wondering of someone could help me with this question :)
 
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  • #2
Do you have any idea yourself? What are you thoughts on this problem? We require some effort from your side before we guide you to the answer.
 
Last edited:
  • #3
What is the derivative of h(x) = 50sin^-1 (0.1x)? That's all this is asking. Do you know the derivative of arcsine?
 
  • #4
is it
1 / sqrt(1-x^2)

:)
 
  • #5
JakePearson said:
is it
1 / sqrt(1-x^2)

:)


yes so now you know

[tex]\frac{d}{dx} (sin^{-1}x)= \frac{1}{\sqrt{1-x^2}}[/tex]

what is d/dx( sin-1(0.1x)) ?
 

FAQ: How Does the Height of a Parachute Change with Horizontal Displacement?

What is the rate of change?

The rate of change, also known as the slope, is a measure of how quickly a variable is changing over a specific period of time or over a given interval.

How do you find the rate of change?

The rate of change can be found by dividing the change in the dependent variable by the change in the independent variable. This can be represented by the formula: (change in y) / (change in x).

What does a positive rate of change indicate?

A positive rate of change indicates that the dependent variable is increasing as the independent variable increases. This means that there is a positive correlation between the two variables.

What does a negative rate of change indicate?

A negative rate of change indicates that the dependent variable is decreasing as the independent variable increases. This means that there is a negative correlation between the two variables.

Why is finding the rate of change important?

Finding the rate of change can help us understand how a variable is changing over time and can be used to make predictions about future values. It is also a fundamental concept in calculus and is used in many real-world applications such as finance, physics, and engineering.

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