MATH 2214 Midterm: MATH 2214 Virginia Tech 2.9 Exam
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Solutions 2. 9: we have the di erential equation which has the solution v = g k m v, v(0) = 0, v(t) = mg k mg k exp( The velocity is half of the terminal velocity when i. e. t = m k ln 2. 2 mv = kv, v(t) = v(0) exp( kt m. We are told that v(0) = 220 mph, t = 4 sec, v(t) = 50 mph, and mg = 3000 lb. Since g = 32 ft/sec2, we nd m = 93. 75 lb sec2/ft. Finally k = m t ln(v(0)/v(t)) = 34. 73 lb sec/ft: the distance traveled is. 0 v(t) dt = v(0) m k (1 exp( . )) = 0. 1274 miles. (do not forget the conversion from hours to seconds here!: we have mv = mg kv, v(0) = v0. The solution of the di erential equation is v(t) = The maximum height is reached when v(t) = 0, i. e. we obtain.
