A roller coaster consists of carts has a mass of 200 kg. A - What is the velocity of the cart at the bottom of the roller coaster if it has a kinetic energy of 160 000J?

B - If 20% of the energy was wasted as heat and sound when the cart rolled down the roller coaster, what was the total gravitational potential energy that the roller coaster started with (g=9.81 N/kg)?

C - What was the height at the top of the roller coaster?

D - If the roller coaster cart gained this gravitational potential energy through a pulley system with a motor, and the motor took 30 seconds to pull the cart from the bottom to the top what was the power of the motor?

For a particular reaction, ? h = -144.6 kj and ? s = -301.2 j/k. calculate ? g for this reaction at 298 k.

The intensity of a polarized electromagnetic wave is 12 w/m^2. part a) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=0∘ with the plane of polarization? part b) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=30∘ with the plane of polarization? part c) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=45∘ with the plane of polarization? part d) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=60∘ with the plane of polarization? part e) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=90∘ with the plane of polarization?

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit