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Three balls with masses 0.5, 0.5 and 1.0 kg and radii 3, 6, and 3 cm, respectively, are simultaneously dropped off the Golden Gate Bridge. How long does it take for each ball to hit the water 227 m below? What are the speeds of the balls when they hit the water? Compare this to the case of no air resistance.

You might wish to enlist Wolfram Alpha to be your mathematical assistant when you evaluate the integral of the velocity to get the distance traveled.

A truck is traveling due west at 30.4 km/h through a rain storm. The wind blows directly east so that the rain comes down making an angle of 10.0° with respect to the vertical. The rain traces on the side windows of the truck make an angle of 54.0° with the vertical (angled toward the rear of the truck). Determine the following.

a) speed of the rain with respect to the Earth

b) speed of the rain with respect to the truck

What is the magnitude of the centripetal acceleration of an object on the surface of the Earth at a latitude of 73.0°? Consider the Earth to be a sphere of radius R = 6.38 ✕ 10^6 m.

A fishing boat in the ocean is moving at a speed of 20.0 km/h and heading in a direction of 40.0° east of north. A lighthouse spots the fishing boat at a distance of 19.0 km from the lighthouse and in a direction of 15.0° east of north. At the moment the fishing boat is spotted, a speedboat launches from a dock adjacent to the lighthouse. The speedboat travels at a speed of 52.0 km/h and heads in a straight line such that it will intercept the fishing boat.

a) How much time does the speedboat take to travel from the dock to the point where it intercepts the fishing boat?

b) In what direction does the speedboat travel? (Express the direction as a compass bearing with respect to due north.)

An object travels in a vertical circle of 1.88 m radius. When the object is traveling downward and is 24.5° from its lowest point, its total acceleration is a = (18.5i + 16.2j) m/s2. At this instant, determine the following. (Take the angle 24.5° clockwise from the axis of the circle that intersects the center and the lowest point. Assume that the +x axis is to the right and the +y axis is up along the page.)

a) magnitude of the radial acceleration

b) magnitude of the tangential acceleration

c) speed of the object

d) velocity of the object (Express your answer in vector form.)

A flat go-kart track consists of two straightways 100 m long with semicircular ends which have a radius of 25.0 m. A go-kart executes the curved end with a constant tangential acceleration while slowing from 13.8 m/s to 5.6 m/s. Determine the magnitude of the total acceleration of the go-kart at the beginning and end of the curve. (Answers should be to two decimal places.)

Consider the Earth to be a sphere of radius R = 6.38 ✕ 106 m.

In order to win the game, a placekicker must make a field goal from a distance of 42.0 m. The regulation height for the crossbar is 2.44 m. The placekicker decides to kick the ball with a speed of 24.2 m/s at an angle of 54.8° with respect to the horizontal.

Two dimensional vectors, A and B, have the same magnitude. The angle of orientation for vectors A and B are respectively θA = 42.0° and θB = 70.0°. The vector C is related to vectors A and B by the relationship C = A − 2B. The magnitude and direction for the vector C are |C| = 5.45 and θC = 272.8°. Determine the magnitude of the vectors A and B. (Assume all angles are measured counterclockwise from the positive x axis.)

I'm a recent high school graduate attending college next year. I met my this girl (a sophomore) last year through a club in school. We ended up dating for about a month before I broke it off over the summer. When we both returned to high school in the fall, I couldn't leave her side. We started dating in November and I eventually fell in love. We made it all the way to June. We went to prom together, but she wasn't allowed to go to after-prom. I went without her and made the biggest mistake of my life--I cheated on her. I realized my mistake approximately 5 seconds after it began and stopped immediately. My now ex-girlfriend wants nothing to do with me, but I can't stand leaving her. Is there anything I can do?

Basically: How and why does Jake change over the course of the novel. Then identify another character and state how and why he/she changes or fails to change.

PLEASE HELP ME!

Why do they change/fail to change?

I already have one teacher, my pre-calculus teacher, to write a letter of recommendation. I was wondering whether it is important to get the second recommendation from a humanities teacher. This is important to me because I can ask my physics teacher for one and we have a great relationship, but I am unsure of my relations with any of my English or Social Studies teachers except for my freshman year history teacher. Please let me know what you recommend that I do.

Nothing too long... brief but good please.

1) A crate with a total mass of 50 kg is initially at rest on a level floor.

a) What is the magnitude of the upward force required to lift the crate with an acceleration of 1 m/s^2?

b) If the crate is being lifted at a constant velocity of 2 m/s, what is the magnitude of the upward force acting on the crate?