Math Question of the Week

I just thought I would post some math problems for those who might enjoy them. Some may be very difficult, some may be very easy.Two hikers walking at the same rate leave a camp at the same time, one going due north, the other due east. After each has gone a mile, the northbound camper turns 15Â° clockwise and the eastbound hiker turns 15Â° counterclockwise. The repeat these turns each successive mile until they meet. How far from camp are they when they meet?

And we'll throw in a calc one too ...

The velocity (in feet/sec) of a a rocket whose initial mass (including fuel) is m is:

Code:

`v = gt + u ln[ m / (m-rt)]; t < m / r`

where u is the sxpulsion speed of the fuel, r is the rate at which the fuel is consumed, and g = -32 feet/secÂ² is the acceleration due to gravity. Find the position equation for a rocket wfor which m = 50,000 lbs, u = 12,000 feet/sec, and r = 400 lbs/sec. What is the height of the rocket when t = 100 sec? (Assuming the rocket was fired from ground level straight up)[

Re: Math Question of the Week

Quote:

Originally Posted by **sploit**

Code:

`v = gt + u ln[ m / (m-rt)]; t < m / r`

where u is the sxpulsion speed of the fuel, r is the rate at which the fuel is consumed, and g = -32 feet/secÂ² is the acceleration due to gravity. Find the position equation for a rocket wfor which m = 50,000 lbs, u = 12,000 feet/sec, and r = 400 lbs/sec. What is the height of the rocket when t = 100 sec? (Assuming the rocket was fired from ground level straight up)[

I'm not sure if I calculated it right. I got approxiamately 8800 feet.

Re: Math Question of the Week

Quote:

Originally Posted by **sploit**

Two hikers walking at the same rate leave a camp at the same time, one going due north, the other due east. After each has gone a mile, the northbound camper turns 15Â° clockwise and the eastbound hiker turns 15Â° counterclockwise. The repeat these turns each successive mile until they meet. How far from camp are they when they meet?

[

If I did it right, they are 6 miles away. I may be off a tenth.

Re: Math Question of the Week

Quote:

Originally Posted by **sploit**

I just thought I would post some math problems for those who might enjoy them. Some may be very difficult, some may be very easy.Two hikers walking at the same rate leave a camp at the same time, one going due north, the other due east. After each has gone a mile, the northbound camper turns 15Â° clockwise and the eastbound hiker turns 15Â° counterclockwise. The repeat these turns each successive mile until they meet. How far from camp are they when they meet?

And we'll throw in a calc one too ...

The velocity (in feet/sec) of a a rocket whose initial mass (including fuel) is m is:

Code:

`v = gt + u ln[ m / (m-rt)]; t < m / r`

where u is the sxpulsion speed of the fuel, r is the rate at which the fuel is consumed, and g = -32 feet/secÂ² is the acceleration due to gravity. Find the position equation for a rocket wfor which m = 50,000 lbs, u = 12,000 feet/sec, and r = 400 lbs/sec. What is the height of the rocket when t = 100 sec? (Assuming the rocket was fired from ground level straight up)[

I'll answer this one when you guys move into the 21st Century and use proper, easily interchangeable units. Feet per second!? Pounds weight!?!? :roll:

:P

Re: Math Question of the Week

Quote:

Originally Posted by **sploit**

I just thought I would post some math problems for those who might enjoy them. Some may be very difficult, some may be very easy.Two hikers walking at the same rate leave a camp at the same time, one going due north, the other due east. After each has gone a mile, the northbound camper turns 15Â° clockwise and the eastbound hiker turns 15Â° counterclockwise. The repeat these turns each successive mile until they meet. How far from camp are they when they meet?

Since they are walking at exactly the same speed, then they will meet after 12 turns. If they are not they may never meet.

Each walker is describing a path that is a regular 24-gon wih unt edges, but the easbound hiker followiing one with the initial edge along the x-axis and the northbound hiker one with the initial edge along the y axis. By symmetry thise 24-gons intersect at the origin and after 12 turns.

Re: Math Question of the Week

Quote:

Originally Posted by **sploit**

And we'll throw in a calc one too ...

The velocity (in feet/sec) of a a rocket whose initial mass (including fuel) is m is:

Code:

`v = gt + u ln[ m / (m-rt)]; t < m / r`

where u is the sxpulsion speed of the fuel, r is the rate at which the fuel is consumed, and g = -32 feet/secÂ² is the acceleration due to gravity. Find the position equation for a rocket wfor which m = 50,000 lbs, u = 12,000 feet/sec, and r = 400 lbs/sec. What is the height of the rocket when t = 100 sec? (Assuming the rocket was fired from ground level straight up)[

Integrate the rocket equaton to find that the height h is given by

h =

You can plut in the given values if you wish to find the specific height at 100 sec.