A truck drives on to an entrance ramp to the Brooklyn-Queens Expressway. The on-

Question

A truck drives on to an entrance ramp to the Brooklyn-Queens Expressway. The on-ramp is 150 m long. The truck enters the ramp with a speed of 5 m/s, and the driver begins to increase her speed in order to merge onto the highway. In order for the truck to reach the end of the on-ramp with a speed of 25 m/s, what must be its acceleration? A car is driving over the Sierra Nevada mountains on Tioga Pass Road, from Mono Lake to Yosemite Valley. The car begins on the shore of Mono Lake at an elevation of 2000 m above sea level. It drives 5.5 km, climbing at an angle of 11degree up, to the top of Tioga pass in 0.5 hours. It then begins driving down the other side, at an angle of 7degree, for 6 km in 0.75 hours, before reaching Mono Lake. (It may be helpful to use: Sin 7degree = 0.122, Cos 7degree = 0.993, Sin 11degree = 0.191, Cos 11degree = 0.982)

Explanation / Answer

1.

Galilei's formula:

v2=v02+2ad ---> a=(v2-v02)/2d=2m/s2

2.

a) v1m=d1/t1=11km/h~3.06 m/s

v2m=d2/t2=8km/h~2.22 m/s

b) The final elevation is: 2000+l1sin(11)-l2sin(7)~2000.3185 km.

l1=5.5 km

l2=6 km

c) vx=(x1+x2)/(t1+t2)=(l1*cos(11)+l2*cos(7))/(t1+t2)

t1+t2=0.5+0.75=1.25 h

vx~9.087 km/h~2.524 m/s.

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