1.A park ranger wanted to measure the height of a tall tree. Theranger stood 9.5

Question

1.A park ranger wanted to measure the height of a tall tree. Theranger stood 9.50 m from the base of the tree; and he observed thathis line of sight made an angle of 65.2° above the horizontalas he looked at the top of the tree. The park ranger's eyes are1.80 m above the ground. What is the height of the tree?
2.A delivery truck leaves awarehouse and travels 2.60 km north. The truck makes a left turnand travels 1.25 km west before making another right turn to travel1.40 km north to arrive at its destination. What is the magnitudeand direction of the truck's displacement from thewarehouse?
2.A delivery truck leaves awarehouse and travels 2.60 km north. The truck makes a left turnand travels 1.25 km west before making another right turn to travel1.40 km north to arrive at its destination. What is the magnitudeand direction of the truck's displacement from thewarehouse?

Explanation / Answer

1. top of the tree is    9.50 * tan65.2 =   20.56 m   above the ranger'sheight so .    height of tree =   20.56 + 1.80 =   22.36 meters . 2.   total north driving = 2.60 +1.40 = 4.00 km .     total west driving = 1.25km .    magnitude of displacement = (4.002 + 1.252 )1/2=   4.19 km .    direction = arctan (4.00 /1.25) =   72.64 degrees north of west

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