1. (20 points) Police use the equation to estimate the speed (s) of a car, in miles per hour, based on the length (x), of its skid marks upon sudden braking on dry asphalt.
a. Solve this equation for d.
b. A motorist is involved in an accident. The skid marks are measured to be 90 + Z (remember, Z represents the last two digits of your IRN) feet long. Estimate the motorist’s speed before braking. Round to the nearest whole number.
c. If you are driving at 60 miles per hour, how long would your skid marks be using this formula. Round to the nearest foot.
d. A common rule of thumb is to leave one car length for each 10 miles per hour that you are driving. If your car is 18 feet long and you are driving at 60 miles per hour, ignoring reaction time, does this give your car enough time to stop if the car in front of you manages to stop instantly (perhaps by hitting a large obstacle in the road)?
2. (20 points) For each planet in our solar system, its year is the time it takes the planet to revolve once around the sun. The equation T2 d-3 = C relates the planet’s year (T) to its average distance to the sun (d).
a. For the earth, T is about 365 days and d is about 149 million kilometers (93 million miles). Using these values, with d in millions of kilometers, and T in days, find C. Round C to be in the form #.## x 10n (write C in scientific notation with two digits after the decimal. Replace each # with a digit and n with an appropriate integer).
b. Using this equation and the value you found for C, find the distance to Uranus whose year is about 30,000 days (round to the nearest hundred million km).
c. Venus is about 108 million km from the sun on average. How long is its year in earth-days (round to the nearest whole day)?
d. The asteroid belt can be found between Mars and Jupiter. Most of the belt lies between 300 and 650 million kilometers from the sun. If you were to discover an asteroid that is 300+Z (remember, Z represents the last 2 digits of your IRN) million km from the sun, how long would its year be in earth-days (round to the nearest whole day)?