The drawing shows an exaggerated view of a rifle that has been ‘sighted in' for a 91.4-meter target. If the muzzle speed of the bullet is v₀ = 475 m/s, there are the two possible angles θ₁ and θ₂ between the rifle barrel and the horizontal such that the bullet will hit the target. One of these angles is so large that it is never used in target shooting. Give your answers as (a) the smaller angle and (b) the larger angle. (Hint: The following trigonometric identity may be useful: 2 sinθ cosθ = sin 2θ.)

I have been able to get to sin2θ = (9.8m/s^2) (91.4m) / (475 m/s)^2 but i am not sure what to do from here and keep getting the answer wrong.

A rocket is launched from rest and reaches a position of (65m, 185m) and a velocity of (195m/s, 555m/s) when it runs out of fuel. From this time, t_bo, it flies a projectile motion path.

1. Find the maximum height above the ground the rocket achieves after running out of fuel
2. Find the time t and position x of the rocket when it hits the ground.

Multichannel detectors like diode arrays and CCDs provide a signal to noise ratio (SNR) advantage by the ability to measure many wavelengths simultaneously—a multiplex advantage. Consider the SNR for a photomultiplier tube (PMT), a diode array (DA), and a CCD. Assume the readout noise (RN) associated with these devices is 0 photoelectrons (pe^-) for the PMT, 1000 pe^- for the DA and 10 pe­^‑ for the CCD. The readout noise is a constant number that does not change with exposure time, and it adds to other types of noise in the measurement. Assume the only other source of noise in these detectors is shot noise from the signal we are measuring.

When we consider both shot and readout noise, the SNR for a signal S(pe^‑) is given by,

SNR = S/(sqrt[S + (RN)²]).

Assume we want to measure a luminescence signal using a spectrometer that collects a signal of 10⁵ pe^-/s at the detector at every wavelength (e.g., ignore quantum efficiency differences in the detectors, which by the way are in reality very large).

1. What is the signal to noise ratio for a PMT measurement of this luminescence, at a single wavelength, for a 1 second exposure? For a 100 s exposure?
2. How long will it take to measure 1024 wavelengths using the PMT, to give a SNR of 300 at each wavelength?
3. For a 1024-pixel diode array and a 1024x1024 pixel CCD, what total exposure time would be needed to give a SNR of 300 at each wavelength? Note: the readout noise is different for these detectors.
4. Unlike the diode array, the CCD also has pixels in the vertical direction. This gives an additional SNR advantage for the CCD detector. Explain why this is?

A 11.0 nC charge is at x = 0cm and a -1.3 nC charge is at x = 5 cm .

At what point or points on the x-axis is the electric potential zero?

Explain the term ‘strain rate sensitive’. Show your references.

A rope exerts an 18-N force while lowering a 20-kg crate down a plane inclined at 20∘ (the rope is parallel to the plane). A 24-N friction force opposes the motion. The crate starts at rest and moves 11 m down the plane.

Part A:  Determine the final speed of the crate. The system consists of the crate, the surface of the incline and Earth.

Part B: Determine the change in gravitational energy.

Part C: Determine the change in kinetic energy.

Part D: Determine the change in internal energy.

Part E: Determine the work done by the rope.

The parameters that determine the performance of cornstarch as thickener. How to determine these parameters？ What equipment is used in determining these parameters?

5) A solid conducting sphere of radius 2.00 cm has a charge of 8.00uC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a charge of -4.00uC. Find the electric field at

a) r= 1.00 cm

b) r= 3.00 cm

c) r= 4.50 cm

d) r= 7.00 cm

from the center of this charge configuration.

A speaker at an open-air concert emits 500 W of sound power, radiated equally in all directions.

Part A:

What is the intensity of the sound 6.8 m from of the speaker?

Express your answer to two significant figures and include the appropriate units.

Part B:

What sound intensity level would you experience there if you did not have any protection for your ears?

Express your answer using two significant figures. Units must be in (dB)

Part C:

Earplugs you can buy in the drugstore have a noise reduction rating of 23 decibels. If you are wearing those earplugs but your friend Phil is not, how far from the speaker should Phil stand to experience the same loudness as you?

Express your answer to two significant figures and include the appropriate units.

1. Given two vectors such as

A⃗ =2x̂ +4ŷ +7ẑ

B⃗ =−3x̂ +8ŷ −2ẑ

what is their sum? What is its length, and what angle does it make to the plane of x and y? What is the dot product A⃗ ⋅B⃗

? What is the dot product of their sum with a unit vector in the z direction (A⃗ +B⃗ )⋅ẑ

? (Hint: this gives the z-component of the sum.).

2. When you apply a force of 100 N to a 25 kg box resting on a table, what is the smallest coefficient of static friction that will give a frictional force sufficient to prevent the box from moving? Suppose you push just a little harder and it starts to move. If the coefficient of kinetic friction is 0.1, how fast will it be going after 2 seconds of pushing?

3. If you walk up a mountain that is 1.5 km high (1500 meters), and your mass is 65 kg (your weight is about 143 lb of gravitational force at Earth's surface), how much energy do you use in joules to overcome Earth's gravity? How much would that be in food calories, where 1 calorie is 4.18 J and a "food" calorie is a kilocalorie in the units used by physicists and chemists. Similarly, if an object of your falls from low Earth orbit to Earth's surface, a distance of say 400 km which is the approximate height of the International Space Station orbit, how much kinetic energy would it have on reaching the Earth's surface -- assuming (a) it starts from rest, and (b) it does not lose energy to the atmosphere on the way down.

This is Introduction to PowerLab

1. a) Describe what is actually being recorded by the PowerLab and displayed in LabChart.

    b.) What is signal conditioning?

What phenomena can be explained using a wave model of light? Do this carefully and thoroughly. Be sure to state what property of the wave model leads to the explanation it provides. Link this property to the ray and Huygen’s diagrams you draw. DRAW DIAGRAM

I want important notes and equations in chapter 4 physics 1
Related topics:

1. contact forces

also for chapter 5:

1. applying newton's laws

2.applying newton's laws with constant-acceleration kinematics

1. A ball is thrown from the top of a 50 m high cliff with a velocity of 10 m/s @ 30o. a. What is the time to the maximum height and what is the max height? b. How long does the ball take to hit the ground? c. What is the velocity of the ball when it hits the ground? d. What is the horizontal range when the ball hits the ground (total x)?

2. Consider the initial velocity given in #1. What is the magnitude of the parallel and perpendicular components of acceleration for this velocity? What is changing faster, the direction or the magnitude of the initial velocity?

Three equal positive point charges of magnitude Q = 10.00μ C are located at three corners of a square of edge length d = 10.5 cm. A negative charge -30.00μ C is placed on the fourth corner. At the position of the negative charge, what is the magnitude of the electric field due to the three positive charges? What is the magnitude of the attractive force on the negative charge?