A stone is dropped from rest into a well. The sound of the splash is heard exactly 1.60 s later. Find the depth of the well if the air temperature is 12.0°C. in m

A train has a mass of 4.82E+6 kg and is moving at 69.9 km/hr. The engineer applies the brakes, which results in a net backward force of 1.91E+6 N on the train. The brakes are held on for 28.2 s. What is the new speed of the train?

How far does it travel during this period?

To become familiar with using the image of one instrument as the object of the next and tracing rays through a system of multiple instruments.

Multiple optics refers to any system of more than one optical instrument through which light passes. Most devices related to optics, such as cameras, microscopes, and telescopes, contain multiple optics systems.

In multiple optics, the image of one optical instrument becomes the object of the next one. Thus, in multiple optics problems, you need to find the image created by the first optical instrument that the rays encounter. Then, you will use that image as the object of the next optical instrument, repeating this pattern until you have followed the rays all the way through the system. It is very important to be alert to the geometry and to signs when you find the object distance for one instrument from the location of the previous instrument's image. Sometimes, the image is formed on the virtual side of the instrument, leading to a virtual object. This may sound strange, but in practice, its effect on your calculations is simply to make the object distance negative instead of positive.

Several optical instruments are placed along the x axis, with their axes aligned along the x axis. A plane mirror is located at x=0. A converging lens with focal length 5.00 m is located at x=12.5m. An object is placed at x=22.5m.

Part A: First, find the location of the image created by the lens by itself (as if no other instruments were present).

ANSWER

Part B: Next, find the location of the image created by the plane mirror (after the light has passed through the lens).

ANSWER

Part C: What is the location of the final image, as seen by an observer looking toward the mirror, through the lens? Keep in mind that the light must pass back through the lens, and thus you must do one more calculation with the thin lens equation.

ANSWER

Part D: First, find the magnitude mlens1 of the magnification of the image created when light from the object passes through the lens the first time (as if the mirror were not present).

ANSWER

Part E: Next, find the magnitude mmirror of the magnification of the plane mirror.

ANSWER

Part F: Now find the magnitude mlens2 of the magnification of the image created when light from the object passes through the lens the second time (after reflecting off the mirror).

Part G: What is the magnitude of the magnification of the final image?

Find the magnitude of the vector sum r of the vector displacements c and d whose components in meters along three perpendicular directions are cx= 7.8, cy= -3.8, cz= -6.4; dx= 4.7, dy= -2.1, dz= 3.7;

A block of mass ?=2.00 kg slides along a horizontal table with velocity ?0=3.50 m/s . At ?=0 , it hits a spring with spring constant ?=42.00 N/m and it also begins to experience a friction force. The coefficient of friction is given by ?=0.300 . How far has the spring compressed by the time the block first momentarily comes to rest? Assume the positive direction is to the right.

1. A beanbag is thrown horizontally from a dorm room window. The height of the window is h = 10 meters above the ground as shown in the figure. If the beanbag

4. Mrs Garcia, a physics enthusiast, goes to a water park in South Padre Island to test the concepts learned during class. She goes on a water slide that is 265 meters long and is built at an angle with the ground of θ = 30 degrees. – What is her final velocity at the end of the slide?

5. A goalkeeper kicks a soccer ball that is initially resting on the ground. She kicks the ball with an initial velocity of 8 m/s. The initial angle between the ground and the trajectory of the ball is θ=27 degrees. – How long is the ball in the air? – How far does the ball travel? – How high does the ball go? Hint: Use equations of motion and the definition of range and maximum height for projectile motion.

6. Solve the following quadratic equations: 2x 2 + 6x + 1 = 0 (1) 4x 2 + 12x + 2 = 0 (2) 9x 2 − 4x + 12 = 0 (3) (x − 1) x + 3 + 3 (x − 1) = (4 − x) (x − 1)(x − 1) (4) Hint: Factor and simplify using (x − 1).

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Accurately describe a field from a dipole (magnetic or electric) and analyze its effects and effects of magnetic/electric fields on them

Explain how a series circuit is different than a parallel circuit in regard to how the resistances (i.e. lights, appliances) are joined together. Then explain if it is more desired to have the wiring in a house based on a series circuit or a parallel circuit and why.

An engraver uses a magnifying glass (f = 7.20 cm) to examine some work, as in the drawing. The image he sees is located 28.0 cm from his eye, which is his near point. (a) What is the distance between the work and the magnifying glass? (b) What is the angular magnification of the magnifying glass?

1.A 65.0 kg object slides down a 30^o angle slope from rest at a height of 15.0 m. The coefficient of kinetic friction between the object and the slope surface is 0.15. (A) What is the object

An infinite number of thin parallel wires are grouped into two sheets. One sheet spans from (x,y) = (- ∞, 5cm) to (x,y) = (+ ∞ , 5cm) and the other spans from (x,y) = (-∞ , - 5cm) to (x,y) = (+ ∞, - 5cm) . These wires all carry a current of 5A out of the page and there are 10 wires per cm.

Determine, in T, the magnetic field in the x direction inside the two sheets at y=0. Include the appropriate sign in your answer

m_earth = 5.9742 x 10²⁴ kg
r_earth = 6.3781 x 10⁶ m
m_moon = 7.36 x 10²² kg
r_moon = 1.7374 x 10⁶ m
d_{earth to moon} = 3.844 x 10⁸ m (center to center)
G = 6.67428 x 10^-11 N-m²/kg²

A 1600 kg satellite is orbitting the earth in a circular orbit with an altitude of 1600 km.

How much energy does it take just to get it to this altitude?

How much kinetic energy does it have once it has reached this altitude?

What is the ratio of the this change in potential energy to the change in kinetic energy? (i.e. what is (a)/(b)?)

What would this ratio be if the final altitude of the satellite were 4500 km?

What would this ratio be if the final altitude of the satellite were 3185 km?

1. A plane is initially 350 km away from Louisville in the direction 30.0◦ north of west traveling due south at a speed of 160 km/hr. Three hours later, the plane is 190 km due south of Louisville traveling at a speed of 150 km/hr in the direction 40.0◦ north of east.

(a) Draw the vector diagram you would use to calculate the average velocity. Make sure you label all your vectors and clearly indicate their direction.

(b) What is the average velocity (including magnitude and direction)?

(c) Draw the vector diagram you would use to calculate the average acceleration. Make sure you label all your vectors and clearly indicate their direction.

(d) What is the average acceleration (including magnitude and direction)?