Applied Problems with
Radical Equations

Solve the following problems that involve radical equations.  Have your graphing calculator handy.  Read carefully to see how the answer is to be expressed.
(Each question is going to ask you to "solve" for a specific variable in the equation.  While this may not be necessary in order to find certain numerical values, it does allow you to practice your skills in dealing with radical equations.)

1.

The formula 
                                             
represents the swing of a pendulum.  S is the time in seconds to swing back and forth, and L is the length of the pendulum in feet.

a.)  How long does it take for a 3 foot pendulum to swing back and forth?  (Round to three decimal places)

b.)  Solve the formula for L.

c.)  Find the length of a pendulum that makes one swing in 2.5 seconds.  (Round to three decimal places.)


 

2.

The speed that a tsunami (tidal wave) can travel is modeled by the equation
                          
where S is the speed in kilometers per hour and d is the average depth of the water in kilometers.

a.) What is the speed of the tsunami when the average water depth is 0.512 kilometers?  (round to nearest tenth)

b.)  Solve the equation for d.

c.)  A tsunami is found to be traveling at 120 kilometers per hour.  What is the average depth of the water? (round to three decimal places)
 


 

3. Isaac Newton established the formula     
             
to calculate the escape velocity from a planet or star.
  • Vesc is the escape velocity
  • G is the Gravitational Constant
  • M is the mass of the planet or star
  • R is the radius of the planet or star

Solve the equation for the radius of the planet or star.

  

 
 


 
 


 

4.

The formula
                         
calculates average velocity of a molecule, atom or ion in a gas at a given temperature.

  • is the average velocity of the particles
  • k is the Boltzmann Constant
  • T is the temperature of the gas
  • m is the mass of the particle

Solve the equation for the Boltzmann Constant.


Note:  In reference to planets, if the average velocity of particles in the atmosphere is greater than the planet's escape velocity (formula in question #3), then the planet will slowly lose its atmosphere to space.

 


 


Roberts