#1
24.) What is the shape of the orbit when the velocity of the satellite is everywhere perpendicular to the force of gravity?

31.) Can a satellite maintain an orbit in the plane of the Artic Circle? Why or Why not?

33.) A high-orbiting spaceshuttle is traveling at 7km/s with respect to the earth. Suppose it projects a capsule at 7km/s rearward with respect to the ship. Describe a path of the capsule with respect to the Earth.

5.) John and Tracy look from their high-rise balcony, which is 80m above the ground, to a swimming pool below - not exactly below, but rather 20m out from the bottom of their building. They wonder how fast they would have to jump horizontally to succeed in reaching the pool. What is the answer?

Thanks in advance.
#3
...keep in mind I am a Buddhist:

Quote by Slavik
24.) What is the shape of the orbit when the velocity of the satellite is everywhere perpendicular to the force of gravity?

There is no orbit, only a very slow spiral towards imminent destruction.


Quote by Slavik
31.) Can a satellite maintain an orbit in the plane of the Artic Circle? Why or Why not?

No satellite can maintain its orbit indefinitely. It, like everything else, will ultimately crash flaming into the surface of the sun.


Quote by Slavik
33.) A high-orbiting spaceshuttle is traveling at 7km/s with respect to the earth. Suppose it projects a capsule at 7km/s rearward with respect to the ship. Describe a path of the capsule with respect to the Earth.

Straight ****ing down, dude! Except without the astrices.


Quote by Slavik
5.) John and Tracy look from their high-rise balcony, which is 80m above the ground, to a swimming pool below - not exactly below, but rather 20m out from the bottom of their building. They wonder how fast they would have to jump horizontally to succeed in reaching the pool. What is the answer?

WTF are John and Tracy doing staring out the window when they should be having gratuitous sex in a variety of positions leading ultimately to a permanent crust of semen encasing the entire bed, videotaping every second of it and posting on it YOUTUBE?

What kind of sorry-ass pimp does John think he is anyway? That's the real question.


Quote by Slavik
Thanks in advance.

You're ****ing welcome.

Can you spell F-A-I-L?!
"Virtually no one who is taught Relativity continues to read the Bible."

#5
Hey man,
I'm pretty sure for #24 that its a circle. Because gravity is always accelerating straight into the earth so as the satellite revolves around the earth, its velocity is 90 degrees to their acceleration.
For #31 you should be able to maintain orbit around the arctic circle if you are moving fast enough but don't quote me on that.
For #33 the orbit will be the same as that of the space ship just higher. The faster the object is moving, the larger its radius.
For #5 its an elementary particle physics question. I assume that you can assume no air friction and gravity is the only force acting. So you know that you have a right triangle 80m by 20m and thus an angle of 76 degrees. The next step is to solve for the time it takes to fall in the Y direction and then take that time you got, plug it into the x direction and find the initial velocity v0 that way.

-Big Pert
#6
I can't answer the first three, but as for the last one (#5), I assume it is a horizontal projection, meaning there is no angle theta. This also means that there is no intial velocity in the y direction, but only acceleration due to gravity, at 9.8 m/s. Use the following equation to find ∆t: ∆y=vi(sinϴ + 1/2a(∆t)^2 In this equation, you can eliminate vi(sinϴ since you know that the initial velocity in the y direction is 0. Now just solve for ∆t. After finding this, use the equation ∆x=(vix)(∆t) to solve for the initial velocity in the x direction, which is what you are looking for. ∆x = 20m, ∆y = 80m. Hope this helped.
#8
Quote by Slavik
24.) What is the shape of the orbit when the velocity of the satellite is everywhere perpendicular to the force of gravity?

Circular dude. Think about it.


Quote by Slavik
31.) Can a satellite maintain an orbit in the plane of the Artic Circle? Why or Why not?

Nope. Gravity is in the wrong direction. Must orbit in a great circle.


Quote by Slavik
33.) A high-orbiting spaceshuttle is traveling at 7km/s with respect to the earth. Suppose it projects a capsule at 7km/s rearward with respect to the ship. Describe a path of the capsule with respect to the Earth.

Down, down, more down, and bang.

Quote by Slavik
5.) John and Tracy look from their high-rise balcony, which is 80m above the ground, to a swimming pool below - not exactly below, but rather 20m out from the bottom of their building. They wonder how fast they would have to jump horizontally to succeed in reaching the pool. What is the answer?

Time t taken to fall 80 m under gravity:

Displacement s = -80 m, initial velocity u = 0, acceleration a = g = -9.8 m s^(-1). Negative vectors are downward motion.

=> s = u . t + 1/2 . a . t^2

=> -80 = 1/2 x -9.8 x t^2

=> t^2 = 16.3

=> t = 4.04 s

Horizontal velocity v necessary to travel 20 m in 4.04 s:

Displacement s = 20 m, time t = 4.04 s.

=> v = s / t

=> v = 20 / 4.04

=> v = 5.0 m s^(-1)
Last edited by Malakian88 at Feb 20, 2008,