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Question

a rider races up two successive straight hills of different slope and length. the first is 2.00 km long at an angle of 5 degrees above the horizontal. this is immediately followed by one 3.00 km long at 7 degrees.

(a )what will be the overall (net) angle from start to finish: (1) smaller than 5 degrees (2) between 5 and 7 degrees (3) greater than 7 degrees.

(b ) calculate the actual overall net angle of rise experienced by this racer from start to finish

Answer 1

(a) between 5 and 7 degrees

(b) 6.20 degrees

All you have to do is make triangles and use sine, cosine, and tangent. You can find out the horizontal distance by adding 2cos5 + 3cos7. Then you can find out the vertical distance by adding 2sin5 + 3sin7. Finally, use inverse tangent on the vertical distance divided by the horizontal distance.