Mechanics | Relativity Answers

Use tiur knowledge of geometry to show that the angle alpha between the worldline of an inertial observer and the light cone(draw in intertial frame using units in which light rays travel at 45 degees) is the same as the angle B between that observer line of simultaneity.

Calculate the size of stelar aberration effect in newtonian physics for light coming straight down at speed c and a telescope moving straight sideway at speed v

An archer fires an arrow towards the wall of a castle. The arrow is fired at 45° from horizontal at a velocity of 22m/s. If the wall is 40m away and stands 7m tall, calculate whether the arrow will drop inside the castle walls.

a) Calculate the maximum height of the arrow
b) Calculate the maximum range of the arrow
c) Calculate the vertical height of the arrow as it reaches the wall
d) Describe the journey of the arrow and whether or not it was successful

The equation of two progressive waves is given by y1 = Asin(kx-wt) and y2 = Asin(kx -wt+θ). Show that
a) y= 2A sin(kx-wt)
b) y= 0

Consider a equation for t below 191×2=3.97t×t+33.4t
What value of t satisfies this equation

Explain the difference between question(a) and (c) as clearly possible.

The brick wall of a house has the square S = 20 m2 and the thickness d = 37 cm. The room inside the house is heated with the electrical heater with power P = 1 kWt. Define the distance from the inner surface of the wall to the plane inside the brick wall where the temperature equals 0t = °0 С, if the temperature outside is t =− ° 26 С. The heat conductivity of the brick is λ = 0,4 Wt/(m⋅К). Other heat losses shall be neglected. The room temperature is the same all over the room.

3. Acceleration [8]
Assume that a car with mass m =1,200 kg accelerates from rest with a constant power (constant change of mv2
energy with time) P = 50. kW. Then the kinetic energy is given by 2 =Pt .
(a) Find the speed as a function of time. [2]
(b) Differentiate the speed to find the acceleration as a function of time. [2]
(c) Assume that the acceleration is limited by the coefficient of friction between the tires and the wet road,
=0.40 . What is the minimum time for the result in part (b) to be valid?

By Donald Marolf's Notes what is relativity and the gravitational field