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.
1 Answer
-
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.
