# Calculating gradient with distance and speed

• Mukilab
In summary, the conversation discusses a physics problem involving calculating the gradient using kinematic equations and trigonometry. The final answer for the gradient is 0.101 and is found by using the sin rule and then taking the tangent of the calculated angle. The conversation also includes a discussion about drawing a diagram to better understand the problem.
Mukilab

Question 11

h=v^2/g

## The Attempt at a Solution

convert 36km/h into 10m/s
10 is final velocity so average should be 5m/s
h=v^2/g=5^2/10=2.5m
Using pythagoras theorem we can calculate that the other length must be roughly 50
(2.5^2+x^2=50^2)

Therefore since the gradient is the change in y over the change in x,
shouldn't the gradient just be 2.5/50=0.05? The actual answer is 0.101, they say the word 'tangent' in the markscheme but offer no explanation for it and I do not understand it.

Any help would be great, thank you very much

you have the final speed and initial speeds 10m/s and 0m/s. You have the distance travelled.

The first thing to do would to be calculate the acceleration and if you look at your kinematic equations

you'll notice the second equation fits what you have

a = vf2/(2d)

you know that the y acceleration is gravity with a value of 9.81m/s^2

you can use trig to find the angle of the gradientsin(theta) = ?

Liquidxlax said:
you have the final speed and initial speeds 10m/s and 0m/s. You have the distance travelled.

The first thing to do would to be calculate the acceleration and if you look at your kinematic equations

you'll notice the second equation fits what you have

a = vf2/(2d)

you know that the y acceleration is gravity with a value of 9.81m/s^2

you can use trig to find the angle of the gradient

sin(theta) = ?

I actually did use that exact formula to find acceleration but I didn't see how it could be used to find a gradient

I found a=1m/s^2

However these are acceleration, so can I still use them to find the gradient?

>Checking
sin(10/1)=0.017

using g=9.81 still gives 0.17 which is also wrong.

.__. where have I gone wrong?

Thank you very much for your help so far

The answer is 0.101 (3 sf) I realized I hadn't mentioned it so far

its been a long long time since I've done this kind of physics

the best thing to do is draw a picture it helps a lot

i drew this but i think i mucked up, that A should be in the top left of the of the large triangle because the angle i go would mean acceleration would be close to g if A was where i drew it.all i know is that i got 84.15 degrees. which i don't think is right and now this will bug me...

but yes the acceleration down the hill is 1m/s

Liquidxlax said:
its been a long long time since I've done this kind of physics

the best thing to do is draw a picture it helps a lot

i drew this but i think i mucked up, that A should be in the top left of the of the large triangle because the angle i go would mean acceleration would be close to g if A was where i drew it.

all i know is that i got 84.15 degrees. which i don't think is right and now this will bug me...

but yes the acceleration down the hill is 1m/s

Can anyone remind me how gradient is related to angles?

Nevermind I figured it out with my friend.

If you use sin rule you can get the angle

then tan of that angle is the gradient.

I appreciate the help, thank you

## FAQ: Calculating gradient with distance and speed

Gradient is a measure of change in a particular variable over a distance or time. It is commonly represented as the slope of a line on a graph.

Gradient is calculated by taking the change in the variable (such as speed) divided by the corresponding change in distance or time. This can be represented as the rise over run on a graph.

## What is the significance of gradient in science?

Gradient is important in science as it helps us understand the rate at which a variable is changing. This can be applied to many different fields, such as physics, chemistry, and biology, to analyze and predict patterns and behaviors.

## What units are used to measure gradient?

The units used to measure gradient depend on the variable being analyzed. For example, the gradient of speed would be measured in units of distance per time, such as meters per second. The gradient of temperature would be measured in units of temperature change per distance, such as degrees Celsius per meter.

## How can gradient be used to analyze motion?

Gradient is commonly used in physics to analyze the motion of objects. By calculating the gradient of an object's speed over time, we can determine its acceleration. This can help us understand the forces acting on the object and predict its future motion.

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