A car is driving over the Sierra Nevada mountains on Tioga Pass Road, from Yosem

Question

A car is driving over the Sierra Nevada mountains on Tioga Pass Road, from Yosemite Valley to Mono Lake. The car begins on the floor of Yosemite Valley, at an elevation of 1600 m above sea level. It drives 10 km, climbing at an angle of 8 Degree up, to the top of Tioga pass in 1 hour. If then begins driving down the other side, at an angle of 10 Degree, for 6 km in 0.75 hours, before reaching Mono Lake. (It may be helpful to use: Sin 8 Degree = 0.139, Cos 8 Degree = 0.990, Sin 10 Degree = 0.174, Cos 10 Degree = 0.985) What is the car's average speed driving from Yosemite Valley to the top of Tioga pass? And, what is the average speed at which the car drives from Tioga Pass to Mono Lake? When the car arrives at Mono Lake at the end of the trip, what is its final elevation? For the full drive, what is the average horizontal velocity?

Explanation / Answer

a)

Average speed while driving up : 10 km/hr
Average speed while driving down : 6/0.75 : 8 km/hr

b)

Initial elevation = 1600m
elevation after driving up = 1600m + 10km*sin(8) = 1390 + 1600 = 2990m
elevation after driving down = 2990 - 8km*sin(10) = 2990 - 1392 = 1598m

c)

Average horizontal velocity = horizontal distance / time =[ 10km*cos(8) + 8km*cos(10) ]/[1+0.75] = 10.16 km/hr

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