# Solve Slope & Y-Intercept for Cliff Height & Time to Top

• 044
In summary, the problem gives limited information about a hiker climbing a cliff at a constant rate of speed. After 2 minutes, he is 160 ft from the bottom, and after 5 minutes, he is 380 ft from the bottom. However, this does not provide enough information to determine the height of the cliff or when the hiker reached the top. The given equation, y = 73.3x + b, does not make sense and the problem seems unrealistic.
044

## Homework Statement

Hiker 1 was at the bottom of a cliff. He started climbing trying to maintain a constant rate of speed. After 2 minutes he was 160 ft from the bottom of the cliff and after 5 minutes he was 380 ft from the bottom. What is the height of the cliff and when did he reach the top?

## Homework Equations

Found slope with m = 380 - 160/5 - 2

y = 73.3x + b or y = 220/3 (x) + b

## The Attempt at a Solution

I found y-intercept to be 13.3 ft which as the height of the cliff doesn't make sense to me. I can think of no way to determine how long to the top going up. I can see how you could calculate the height and time going down, but not up.

044 said:

## Homework Statement

Hiker 1 was at the bottom of a cliff. He started climbing trying to maintain a constant rate of speed. After 2 minutes he was 160 ft from the bottom of the cliff and after 5 minutes he was 380 ft from the bottom. What is the height of the cliff and when did he reach the top?

## Homework Equations

Found slope with m = 380 - 160/5 - 2
Please use parentheses. What you should write is m = (380 - 160)/(5 - 2).
044 said:
y = 73.3x + b or y = 220/3 (x) + b

## The Attempt at a Solution

I found y-intercept to be 13.3 ft which as the height of the cliff doesn't make sense to me. I can think of no way to determine how long to the top going up. I can see how you could calculate the height and time going down, but not up.

Is this the exact wording of the problem? If so, it doesn't seem to me that you are given enough information to answer the question. All you know is that at 2 minutes he has climbed 160 feet, and after 5 minutes, he has climbed 380 feet.

BTW, this seems to me to be a problem cooked up by someone who has no notion of rock climbing. (If you are climbing a cliff, you are rock-climbing, not hiking.) If the climber could maintain the pace he had in the first two minutes, he would be climbing 80 ft/min., or 4800 ft/hour. I don't think anyone could do this.

## What is the formula for solving slope and y-intercept for cliff height and time to top?

The formula for solving slope and y-intercept for cliff height and time to top is y = mx + b, where y represents the cliff height, x represents the time to reach the top, m represents the slope, and b represents the y-intercept.

## How do I calculate the slope and y-intercept for a cliff?

To calculate the slope and y-intercept for a cliff, you will need to have two points on the cliff. Use the formula (y2-y1)/(x2-x1) to calculate the slope, where y2 and y1 are the y-coordinates of the two points and x2 and x1 are the x-coordinates. Then, use the formula b = y - mx, where b is the y-intercept, y is the y-coordinate of one of the points, m is the slope, and x is the x-coordinate of the same point.

## Can I use this formula to calculate the height and time for any type of cliff?

Yes, you can use this formula to calculate the height and time for any type of cliff as long as you have two points on the cliff to use in the calculations.

## Is this formula accurate for cliffs with a curved or angled surface?

Yes, this formula is accurate for cliffs with a curved or angled surface as long as you use two points that are on the same curve or angle to calculate the slope and y-intercept.

## Are there any limitations to using this formula for calculating cliff height and time to top?

One limitation of using this formula is that it assumes the cliff has a constant slope and does not take into account any changes in slope along the way. It also assumes that the cliff is a straight line, so it may not be accurate for cliffs with complex shapes or features. Additionally, it does not account for factors such as wind or other environmental conditions that may affect the time it takes to reach the top of the cliff.

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