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Expert: - 11/10/2008


Question
Mike and Sarah are playing a fun game in which they spin around on an office chair while holding a rubber band ball and then let it go. The object of the game is to hit a light switch on the wall and turn off the lights. Sarah, who gets dizzy easily, decides to do some math to help her win the game quickly. The chair has a radius of 1.5 feet and Sarah spins once around every 3 seconds. When she starts her spin, the wall is directly to Sarah's left, 12 feet away. The light switch is 5 feet further down the wall.
a) When should Sarah release the ball?
b) At what angle will the chair be in reference to the starting point?
c) What speed is the ball traveling when it hits the wall?
d) What is the vertical and horizontal components of the ball's velocity?

Answer
a) Assuming she is spinning sideways and releasing the ball of the side of the chair, we have a triangle with leg 1.5' and hypoteneus 12'.  The length of the leg that the ball travels down is
√(12²-1.5²) = √141.75.  To find the time to release the ball, compute the the angle such that sec(Θ) = 12/1.5 = 8.  Once this has been done, subtract that amount from π radians to get the angle she releases it at from the beginning.  To get the time, take this value times 3 over 2π.

b) We assumed the ball was released from the edge of the chair.  The speed of the ball is given by (1.5*2*π/3) ft/s = π ft/sc.  The height of the ball is given by distance of the ball is πtcos(Θ). The height of the ball is given by πtsin(Θ)-16t².  Θ needs to be chosen so that the height is at -5 when the horizontal distance is at the long leg on our triangle.

c) The speed will be the √(π²+v²) where v is the vertical speed when it hits the wall.

d) The vertical and horizontal componets of velocity are the speed multiplied by by cos(Θ) and sin(Θ), respectively, where Θ is the angle it hits the wall at.

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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