A star of mass 7 × 10³⁰ kg is located at <6 × 10¹², 3 × 10¹², 0> m. A planet of mass 9 × 10²⁴ kg is located at <5 × 10¹², 5 × 10¹², 0> m and is moving with a velocity of <0.9 × 10⁴, 1.5 × 10⁴, 0> m/s.

a/ During a time interval of 1 × 10⁶ seconds, what is the change in the planet's velocity? (in xyz vector form)

b/ During this time interval of 1 × 10⁶ seconds, what is the change in the planet's position?(in xyz vector form)

Describe how to improve the efficiency of a room related to heat loss.

Heat transfer can occur through conduction, radiation, and convection.

A projectile is fired with an initial speed of 37.1 m/s at an angle of 44.2 ∘ above the horizontal on a long flat firing range. A)Determine the maximum height reached by the projectile.B) Determine the total time in the air. C)Determine the total horizontal distance covered (that is, the range). D)Determine the speed of the projectile 1.70 s after firing.

A wire of length L has a rectangular cross-section with height H and width W. The wire has a hole all the way through it of area a. The wire is made of material with constant resistivity ρ1 . A battery with a known voltage is applied across the ends of the wire. a. Find the electric field inside the material and the current flowing through the wire. b. If the hole is totally filled with a material that has resistivity ρ2 , what will be the electric field everywhere inside the wire, and what current will flow through the wire?

The outside diameter of the playing area of an optical Blu-ray disc is 11.75 cm, and the inside diameter is 4.50 cm. When viewing movies, the disc rotates so that a laser maintains a constant linear speed relative to the disc of 6.70 m/s as it tracks over the playing area.

What is the average angular acceleration of a Blu-ray disc as it plays an 3.5-h set of movies? (Assume the disk is scanned starting at its inner radius moving outward. Express your answer to two significant figures.)

A 27 g ball is fired horizontally with speed v₀ toward a 106 g ball hanging motionless from a 1.13-m-long string. The balls undergo a head-on, perfectly elastic collision, after which the 106 g ball swings out to a maximum angle θ_max=57^°. What was v₀?

(5) Describe the consequences of a 10-km asteroid striking Earth?

Question 7 a. The radius of curvature of a plano-convex lens is measured to be 2 metres, and the focal length in air (n = 1) is measured to be 4 metres. i. What is the power of the lens? [2 marks] ii. What is the refractive index of the lens material? [4 marks] b. A toy Dalek is placed 40 cm in front of a converging lens of focal length f1 = 20 cm; another converging lens 60 cm behind the first has a focal length of f2 = 10 cm. i. Draw a ray trace diagram for this optical system [4 marks] ii. Show where the image produced by the first lens appears on your diagram. Is it a real or virtual image? [3 marks] iii. What is the magnification of the object at the first image? [1 marks] iv. Show where the final image appears on your diagram. Is it a real or virtual image? [3 marks] v. What is the magnification of the first image at the final image? [1 mark] vi. What is the magnification of the object at the final image? [2 marks]

An unmarked police car traveling a constant 80.0 km/h is passed by a speeder traveling 115 km/h . Precisely 1.50 s after the speeder passes, the police officer steps on the accelerator; if the police car's acceleration is 2.50 m/s2 , how much time passes before the police car overtakes the speeder after the speeder passes (assumed moving at constant speed)?

1. What is total internal reflection and why is it important in optical fibers? What is the critical angle?

2. Does a diverging lens have a focus point?

3. What type of lens, diverging or converging, would you use for a magnifying glass? Explain.

A sphere with a diameter of 70 cm is held at a temperature of 290

As a coffee enthusiast you wish to keep your coffee as hot as possible for as long as possible. You wish to find the rate of heat loss of a typical coffee mug. Assume the mug to be a cylinder which has a lid made out of the same material as the rest of the cylinder, and the thickness of the walls is 1.34 cm. If the coffee in the mug is 79.2 °C and the room temperature is 24.0 °C how much more heat does the mug lose through conduction than from radiated energy. See the hint below for important constants.

Assume that the thermal conductivity of all sides of the mug is 0.850 W/m·C, that the mug has an emissivity of 0.760 and the Stefan-Boltzmann Constant is 5.67 × 10-8 W/m2·K4. Remember to properly convert all units and to include all surfaces of the mug.

A 0.36-kg object connected to a light spring with a force constant of 23.4 N/m oscillates on a frictionless horizontal surface. The spring is compressed 4.0 cm and released from rest. (b) Determine the speed of the object when the spring is compressed 1.5 cm. (d) For what value of x does the speed equal one-half the maximum speed?

A 31.0-kg child on a 3.00-m-long swing is released from rest when the ropes of the swing make an angle of 31.0° with the vertical.

(a) Neglecting friction, find the child's speed at the lowest position.

(b) If the actual speed of the child at the lowest position is 2.50 m/s, what is the mechanical energy lost due to friction?