Atypical set of stairs is angled at 38 degrees. you climb a set of stairs at a speed of 3.1m/s. 1.) how much height will you gain in 4.4 seconds? 2.) how much horizontal distance will you cover in 4.4 second

This one is easy once you see that this can be represented by a vector diagram. Believe it or not, vectors are really really simple to do once you know this neat trick i'm about to show you. It's based on the SOH, CAH, TOA system but is a brilliant for very quickly solving the problem. Imagine the vertical part is the y component and the horizontal part is the x component.

To find the 'x' component, use:
x = V * cos(Ф)
to find the y component, use:
y = V * sin(Ф)

where V = the vector length (here this is calculated as (3.1m/s x 4.4s),
and,
Ф = the angle of the stairs.

If you break down all vector type questions into these parts you will solve them very quickly which is very useful in an exam :)

Let me know if you have any questions, since i have assumed some knowledge in my answer.

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