(10%) Problem 12: The ballistic pendulum was invented in 1742 by English mathematician Benjamin Robins. It consists of an initially stationary pendulum that moves after being struck by a bullet, and it is used to measure the original velocity of the bullet. The known variables are the bullet's mass m, the Pendulum's mass M, and the height to which the block and bullet swing, determined by the length of the pendulum L and final angle θ.

You are traveling in a car going at a constant speed of 100km/h down a long, straight highway. you pass another car going in the same direction which is traveling at a constant speed of 80km/h. as measured from your car's reference frame this other car is traveling at −20km/h. what is the acceleration of your car as measured from the other car's reference frame? what is the acceleration of the other car as measured from your car's reference frame?

Aspacecraft that renters the earth’s atmosphere drastically slows down. the amount of kinetic energy the spacecraft has as it reenters the earths atmosphere

For the below questions, consider a consumer that consumes two goods, x and z with the following utility function. u with bar on top space equals space x to the power of 1 third end exponent z to the power of 2 over 3 end exponent suppose initial values for income and the prices of goods x and z are y equals 90, p subscript x equals space 10, and p subscript z equals 15 respectively, then the price of good x falls to syntax error from line 1 column 89 to line 1 column 100. unexpected '\'.. what is the magnitude of the total effect