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# mid1_sol - Name Student ID S10 PHY321 Midterm 1 NOTE Show...

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Name: Student ID: S10 PHY321: Midterm 1 February 10, 2010 NOTE: Show all your work. No credit for unsupported answers . Moreover, the work can earn you credit for problems that are not fully completed! Turn the front page only when advised by the instructor! Total points for this exam: 25

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1. For the two vectors ~ A = 3 ˆ i - 4 ˆ k and ~ B = 7 ˆ j , find (a) [2 pts] ~ A × ~ B (b) [2 pts] the angle between ~ A and positive direction of the z -axis. 2. [5 pts] In the vicinity of a peak at ( x, y ) = (0 , 0), the elevation for a hill, in terms of coordinates x and y , is given by z = 100 - 0 . 5 x 2 - y 2 - x y . In this expression, x , y and z are in meters. In which direction is the slope at ( x, y ) = (2 , 3) the steepest? Note: You can specify this direction by giving its angle measured clockwise from the x -axis. Alternatively, you may provide a unit vector pointing in that direction. (Over)
3. A moving car is subject to a friction force from the wheels and the ground, approximately independent of the car’s velocity v , and sub- ject to an air drag force that increases with v . Assume that the net resistance force, opposing the car’s motion, may be represented

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mid1_sol - Name Student ID S10 PHY321 Midterm 1 NOTE Show...

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