Please answer these questions:

1) A man stands on the edge of the roof of a 15.0-m tall building and throws a rock with a speed of 30.0 m/s at an angle of 33.3⁰ above the horizontal. Ignore air resistance. Calculate: the total time that the rock spends in the air?

2) A ball is thrown upward at an unknown angle with an initial speed of 20.0 m/s from the edge of a 45.0-m-high cliff. At the instant the ball is thrown, a woman starts running away from the base of the cliff with a constant speed of 6.00 m/s. The woman runs in a straight line on level ground, and air resistance acting on the ball can be ignored. At what angle above the horizontal should the ball be thrown so that the runner catches it just before it hits the ground, and how far does the woman run before she catches the ball?

The majority of exoplanets are gas giants. Are rocky planets (Earth) rare? Explain.

Consider an electron at a distance of 0.053 nm from a proton. Take the origin of coordinates to be at the position of the proton. Let the electron be undergoing uniform circular motion.

A) Find the time-rate-of-change of the angular momentum of the electron.

B) Find the kinetic energy of the electron.

C) Find the potential energy of the electron.

D) Find the total energy of the electron.

According to the Faraday effect, it responds:
a) Explain what it is.
b) Find the index of refraction for right and left circular polarized light.
c) Determine the Verdet constant.
d) explain how it can be verified experimentally.

A stick is resting on a concrete step with 1/6 of its total length ? hanging over the edge. A single ladybug lands on the end of the stick hanging over the edge, and the stick begins to tip. A moment later, a second, identical ladybug lands on the other end of the stick, which results in the stick coming momentarily to rest at θ=62.1∘ with respect to the horizontal, as shown in the figure.

If the mass of each bug is 3.43 times the mass of the stick and the stick is 12.7 cm long, what is the magnitude of the angular acceleration ? of the stick at the instant shown?

Describe the process of convolving an image with a mask (kernel). How could the process be implemented in the (spatial) frequency domain?

Show that Maxwell's displacement current must be introduced to satisfy continuity equation using Gauss' Law, Ampere-Maxwell law and the fact that divergence of a curl of a vector is 0.

Using plane waves, find the Fresnel and Snell formulas. (Reflection and refraction) Show that in a vacuum plane waves propagate orthogonally to each other, and are transverse to the direction of propagation.

•• A meter stick is moving with speed relative to a frame S. (a) What is the stick’s length, as measured by observers in S, if the stick is parallel to its velocity v? (b) What if the stick is perpendicular to v? (c)What if the stick is at to v, as seen in the stick’s rest frame? [HINT: You can imagine that the meterstick is the hypotenuse of a 30–60–90 triangle of plywood.] (d) What if the stick is at 60° to v, as measured in S?

Not hand-writing please (only if it is very clear).

I only need part c and d.

A 75 kg mountain climber hangs stationary from a bungee cord over a steep incline of 80◦ (nearly a vertical wall). The bungee cord has a Hooke constant of k = 550 N/m and is parallel to the incline.

(a) If the climber has a coefficient of friction μs = 0.9 with the incline, how much will the rope deform? Assume that the maximum amount of friction (and thus the minimum deformation).

(b) Suppose the climber loses their grip, reducing this coefficient to only μs = 0.1. Once they come to a stop, what is the rope’s new deformation? Again assume the maximum amount of friction.

there is no figure given

I need a proper solution for this question ( well explained and understandable writing)

Charged particles from outer space, called cosmic rays, strike the Earth more frequently near the poles than near the equator. Why?

In an Otto cycle air is compressed from an initial pressure 120 kPa and temperature 370 T (K). The cycle has compression ratio of 10. In the constant volume heat addition process 1000 kJ/kg heat is added into the air. Considering variation on the specific heat of air with temperature, determine,

(a) the pressure and temperature at the end of heat addition process (show the points on P-v diagram)

(b) the network output

(c) the thermal efficiency

(d) the mean effective pressure for the cycle.

The gas constant of air is R = 0.287 kJ/kg.K

(Describe the necessary assumptions you have considered in your solutions.)