AP Physics?

Test Preparation AP Test Preparation
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<li>Later in the semester we will calculate the escape velocity from various astronomical bodies. The escape velocity is the minimum initial velocity, directed vertically upwards at some distance R from the center of a planet (or asteroid, star, etc.), that enables an object to coast away (i.e. escape) from that planet. Here, we will estimate the escape velocity from the earth using only unit analysis. The two physical quantities that we will use are g, the acceleration due to gravity at the earth’s surface, and R, the diameter of the earth. Using these two quantities, construct a formula with units of velocity, as an estimate for the escape velocity from the surface of the earth. (Note- your estimate, based on nothing but units, is off by only about 40% from the actual answer, which requires a detailed and fairly complex integration).</li>
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<p>(Use an upper case R and a lower case g in your answer).</p>

<p>[What in the world is this question talking about? Can someone explain what to do?]</p>

<li>Due to several previous unfortunate encounters with law enforcement, your car has been equipped with a GPS tracking device. You know that this device radios your current position to police headquarters at precisely hour intervals, but you don’t know the exact time at which this occurs (i.e. it could be every hour on the hour, or every hour on the quarter hour, or something else). If the police can prove that you’ve driven faster than 100 km/hr at any point, then you are busted.</li>
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<p>You have been driving from State College to Sandy Springs, Utah (the latest hot Spring Break destination) along a perfectly straight road for several hours at a leisurely constant speed of 80 km/hr. Sandy Springs is only 49 km ahead. You realize that you can now speed up for the remainder of the trip, without getting busted.</p>

<p>What is the maximum average speed at which you can finish the drive to Sandy Springs, with no chance of getting busted by your GPS tracker?</p>

<p>[At first, I tried using d = 1/2 (v0 +v)t since we don’t know the acceleration. But we don’t even know the time, so I tried using v^2=v0^2 +2ad, but we still don’t know the acceleration. I’m starting to think that this problem requires more than 1 kinematics equation. But I don’t know which ones. Can someone please help me?]</p>

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<h1>4 Since this is based solely on units, we note that R is a length which is in meters and g is measured in meters/second^squared, and velocity is meters/second. We want to use R and g in such a way as to yield meters/second. One way I can see to do this is to calculate Rg and then take the square root, so it is (Rg)^0.5. You could also find the circumference, which is (pi)R and mulitply that by g, then take the square root, so two possible answers are (Rg)^0.5, or [(pi)Rg]^0.5</h1>

<p>I'll look at the other question later</p>