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# Point) body of mass kg is projected vertically upward with an initial velocity 31 meters per second.We assume that the forces acting on the body are the force of gr...

## Question

###### Point) body of mass kg is projected vertically upward with an initial velocity 31 meters per second.We assume that the forces acting on the body are the force of gravity and retarding force of air resistance with direction opposite to the direction of motion and with magnitude clv(t)| where =0.25* and u(t) is the velocity of the ball at time The gravitationa constant is g 9.8mls?a) Find differential equation for the velocity v:(-0.25/4)v-9.8b) Solve the differential equation in pan a) and find f

point) body of mass kg is projected vertically upward with an initial velocity 31 meters per second. We assume that the forces acting on the body are the force of gravity and retarding force of air resistance with direction opposite to the direction of motion and with magnitude clv(t)| where =0.25* and u(t) is the velocity of the ball at time The gravitationa constant is g 9.8mls? a) Find differential equation for the velocity v: (-0.25/4)v-9.8 b) Solve the differential equation in pan a) and find formula for the velocity at any time u(t) 187.8e^(-t/16)-156.8 Find formula for the position function at any time if the initial position is s(0) s(t) = 3002.88(e^(t/16)-1)-156.8t How does this compare with the solution to the equation for velocity when there is no air resistance? If c = 0 then v(t) = 31 - 9.8t, and s(0) = 0, then s(t) = 31t - 4.91?_ We then have that U(t) = 0 when ~3.163 and 5(3.163) ~ 49.031, and that the positive solution to s(t) = 0 is t ~ 6.326, which leads to 0(6.326) 31 meters per second

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