A 500-g ball is dropped from the surface of a tank of water at a speed of 2 m/s. The water exerts on the ball a resistance force that is proportional to the instantaneous speed. If it is known that the maximum speed of the ball is 11 m/s and if the acceleration due to gravity is 9.8 m/s2. Determine the position of the ball at time t, with t in seconds. To find the position of the ball at time t, a student decides to solve the previous problem, and poses the initial value problem: |-6) Where you can see a differential equation with an absent independent variable, to do this, carry out the change of variable v(t) = x'(t) => v'(t) = x' "(t), which transforms the differential equation of second order in the differential equation: v'(t)+2av(t)=9,8 At the end of the process, he obtains the solution of the initial value problem (7), which is: x(t)=11t-(495/49)e^(-49t/55) + (495/49) -(ii) In relation to the scheme of the solution proposed by the student to solve the initial value problem (i), do the following: (a). Determine, using only the techniques for

A 500-g ball is dropped from the surface of a tank of water at a speed of 2 m/s. The water exerts on the ball a resistance force that is proportional to the instantaneous speed. If it is known that the maximum speed of the ball is 11 m/s and if the acceleration due to gravity is 9.8 m/s2. Determine the position of the ball at time t, with t in seconds. To find the position of the ball at time t, a student decides to solve the previous problem, and poses the initial value problem: |-6) Where you can see a differential equation with an absent independent variable, to do this, carry out the change of variable v(t) = x'(t) => v'(t) = x' "(t), which transforms the differential equation of second order in the differential equation: v'(t)+2av(t)=9,8 At the end of the process, he obtains the solution of the initial value problem (7), which is: x(t)=11t-(495/49)e^(-49t/55) + (495/49) -(ii) In relation to the scheme of the solution proposed by the student to solve the initial value problem (i), do the following: (a). Determine, using only the techniques for

Name: A 500-g ball is dropped from the surface of atank of water at a speed
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Description: A 500-g ball is dropped from the surface of atank of water at a speed of 2 m/s. The waterexerts on the ball a resistance force that isproportional to the instantaneous speed. If it isknown that the maximum speed of the ball is 11m/s and if the accel

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter4: Motion In Two And Three Dimensions

Section: Chapter Questions

Problem 75P: A boat can be rowed at 8.0 km/h in still water. (a) How much time is required to row 1.5 km...

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