1.a. Rationalize the denominator in the expression . t =- 2d a Answer: b. Use the rationalized expression from part a. to calculate the time in seconds that a cliff diver is in free fall. Assume the acceleration due to gravity, a, is -9.81 m/s and the dive distance, d, is -35 m. The negative numbers indicate the direction is downward. Round the answer to two decimal places. Answer: c. Use the formula to calculate the velocity of the diver in km/h when she v = - 3.6 2ad or he hits the water. Round the answer to one decimal place. Answer: 2. What are the restrictions, if any, on values for the variables in the following radical expressions? a. 5- x Answer: b. 7- n +8 Answer: c. 6y - 5 + 2 Answer: d. 4- t 3t Answer: 3. As a jet aircraft exceeds the speed of sound the jet sets up a shock wave that may be heard as a sonic boom if the shock wave occurs close to Earth. The speed of sound varies with the temperature. The following formula is for the speed of sound in km/h, based on the temperature of the gas in degrees Kelvin and the molecular mass of the gas in grams per mole: s = 389 T m a. If the average molar mass of a normal air mixture is 28.8 g/mol, what is the speed of sound at an altitude of 4.9 km where the temperature is 256 K (-17C)? Answer: b. What is the speed of sound in helium if the temperature is 300 K (27C). The molar mass of helium is 4.0 g/mol. This is related to why your voice sounds so funny when you breathe helium from a balloon. Answer: c. Rearrange the formula to isolate the temperature, and then calculate the temperature at which the speed of sound in a normal air mixture is 1000 km/h. Assume the average molar mass of the air molecules is 28.8 g/mol. Answer: 4. The time for one complete orbit of a planet around a star can be calculated from the equation . The average radius, in kilometres, of the planet's orbit is r, and T = Kr 3 K is a constant that changes depending on the mass of the star. a. Rearrange the equation to isolate K. Then calculate for K for Earth's solar system knowing that Earth takes one year to go around the sun and that the radius of Earth's orbit is 1.49 108 km from the sun. Answer: b. Calculate how many Earth years it takes Neptune to complete an orbit. Neptune's average orbital radius is 4.5 109 km.