17. A parallel-plate capacitor has space between the plates filled with four slabs of dielectric. The dielectric constant of each slab is indicated in the figure below on the next page. Each slab has thickness d/2, where d is the plate separation. What is the capacitance of the parallel-plate capacitor?

(A)
(B)
(C)
(D)
(E)

1. Given the velocity of a car in two dimensions: = (t²-1, 3). The car starts out at position (x, y) = (2, 4) at t = 0. What is the car at t = 3? (A) (6,9) (B) (8,3) (C) (10,7) (D) (8,13) (E) none of the above.

2. An airplane flies at an altitude of 0.5 km and a speed of 360 km/h. At what horizontal distance x should it release a bomb to hit a target that is moving with constant velocity 90 km/h? (Approximate the gravitational acceleration g by 10 m/s² throughout this test) (A) 500 (B) 750 (C) 250 (D) 1000 (E) none of the above.

3. A boy wishes to row across a river in the shortest possible time. He can row at 2 m/s in still water and the river is flowing at 1 m/s. At what angle with respect to the water velocity should he point the bow (the front of the boat)? (A) 30° (B) 45° (C) 60° (D) 90° (E) none of the above.

4. Two blocks of mass 25 kg and 75 kg are connected by a light rope across a fixed pulley of radius 50 cm and moment of inertia I = 10 kg·m². Assume that the rope never slips. What is the magnitude of the acceleration of the 75 kg block? (A) 0.54 m/s² (B) 0.1 m/s² (C) 0.049 m/s² (D) 0.8 m/s² (E) none of the above.

5. A rope is used to pull a 10 kg box with constant velocity across the floor with coefficient of kinetic friction μk = 1/√3. At what angle (in degrees) is the force F least? (A) 30 (B) 45 (C) 60 (D) 0 (E) none of the above.

6. My weight is mg and the maximum speed my jump is v₀. If I jump off a cart of mass M that can move without friction, what is my maximum horizontal displacement via adjusting the angle of my jump? Note that v₀ is now measured relative to the car. (A) (B) (C) (D) (E) none of the above.

7. An object of mass m that is initially at rest slides down from the top of a smooth sphere (of radius R). If the size of the object is negligible, at what angle θ will it detach from the sphere? (A) cosθ = 1/2 (B) sinθ = 1/2 (C) sinθ = 2/3 (D) cosθ = 2/3 (E) none of the above.

8. A uniform soda can of base area A = 12 cm², mass m = 10 g and height h = 20 cm is filled with soda of density ρ = 1 g/cm³. Use x to denote the height of the remaining soda; find the x that makes the center of mass of the whole system the lowest. It occurs when the soda is (A) half-filled (B) less than half, but more than a quarter filled (C) less than a quarter filled (D) completely empty (E) none of the above.

9. A 10 kg monkey climbs up a light rope that runs over a frictionless tree limb and back down to a 20 kg package on the ground. What is the least acceleration the monkey must have if it is to lift the package off the ground? (A) g/4 (B) g/2 (C) g (D) 2g (E) none of the above.

10. A block of mass m = 10 kg slides from vertical height h = 1 m down a slope of angle θ = π/3 and kinetic friction coefficient μk = 0.5. At the foot of the slope lies a spring of constant K = 200 nt/m. What is the maximum compression of the spring? (A) 1 (B) 1.5 (C) 2 (D) 2.5 (E) none of the above.

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