Question

this is differential equations practice problem

part d should be t = 0,

thank you in sdvancdd!

1. An object of mass m is fired vertically upward with an initial speed of vo. Suppose the air resistance is proportional to the square of velocity. Let k > O be the constant of proportionality. Use g as the acceleration due to gravity. Let v(t) be the velocity at time t. a) Write down the differential equation in effect for v(t) until the object reaches its maximum altitude. b) Solve the DE in (a) for v(t). c) At what time t does the object reach it maximum altitude? d) What is the maximal solution interval ( 10)

Answer 1

e) By Newton's 2nd Law; na dr mg + kr 2 mgt kv 2 mg at 6 So, m dy fat mg+kr2 6 Ś du mg ve +2 oth ton k k mg mg (rything - tai to- th +) مه kg tan t k k where - tan V. mg c) At maximum altitude rits=0 K No kg mg Hong to = tan vo kg mg d) The maximal solution interval can be found by taking a look at solution in (bl. As v 70, ta to & maximal solution interval is [o, to where to is time we got in part (c) so so ]