a. A ball is thrown off a 30 meter tall cliff at an angle of 45 degrees above the horizon. If the ball hits the ground at a speed of 25 meters per second, what was the initial speed of the ball when thrown off the cliff, in meters per second? Assume no air resistance and use g = 10 meters per second squared.

This is a simple "conservation of energy" problem pretending to be something complex. The short answer is that the direction you throw the ball doesn't matter. We know that:

1. The energy when the ball hits the ground is E = 1/2 M V² where M is the (arbitrary) mass of the ball and V is 25 m/sec.
2. the sum of the energy with which it is launched.
3. Initially the ball has an unknown kinetic energy.
4. Initially the ball has potential energy equal to being hoisted up 30 meters to the top of the cliff

b. A sample of gas at a temperature of 300 K is composed entirely of hydrogen gas. If each H₂ molecule in the sample is replaced by a molecule of oxygen gas moving at the same speed, then, rounded to the nearest hundred, what will be the new temperature (in Kelvin) of the sample?

?

c. What is the SI unit for magnetic flux?

The Weber (Wb).

Solution:

ciphertext = Y H Q A G X W Q R M T T T I L N S R A F F T E C N W R Q N M U R Q S B I E Z T
Key        = F A M A T F A M A T F A M A T F A M A T F A M A T F A M A T F A M A T F A M A
plaintext  = T H E A N S W E R T O T H I S I S F A M A T S C U R R E N T P R E S I D E N T