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Josh is climbing up a steep 24* slope, moving at a steady 0.95 m/s along the ground. How many meters of elevation does he gain in one minute of this climb?

I’m not sure how to set the problem up to solve it.

• I presume you mean a 24° slope:

Anyhow, sketch a diagram to illustrate the problem:

….. it will be a right angled triangle with:

a horizontal base labelled A (for Adjacent);

a vertical side (e.g. at RH end of base) labelled O (for Opposite);

a third side labelled H (for Hypotenuse) linking the LH end of the base to the top of the “opposite” side;

The angle between the base and the hypotenuse should be marked as 24°, and a stick figure labelled “Josh” should be placed somewhere on the hypotenuse, with an arrow indicating that he is walking up the slope.

distance walked = velocity x time = 0.95 m/s x 60 s = 57 m

….. (where 60 s = one minute) ;

Now change the “H” to read “H = 57 m” on the diagram.

The elevation gained during Josh’s perambulation is the same as the length of the vertical side marked “O”, and it can be calculated by simple trigonometry :

sin( 24° ) = Opposite / Hypotenuse

⇒ H sin( 24° ) = O ………………………[ multiplying both sides by H ]

⇒ O = 57 x 0.4067 ≅ 23.2m ……….. [ evaluating ]

Now change the “O” to read “O ≅ 23.2 m” on the diagram.

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