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(1 point) A body of mass 7 kg is projected vertically upward with an initial velocity 19 meters per second. We assume that the forces acting on the body are the force of gravity and a retarding force of air resistance with direction opposite to the direction of motion and with magnitude clu(t) | where c = 0.5- and v(t) is the velocity of the ball at time t. The gravitational constant is g = 9.8m/s?. a) Find a differential equation for the velocity u: du dt -9.8-.5v/7 b) Solve the differential equation in part a) and find a formula for the velocity at any time t: v(t) = Find a formula for the position function at any time t, if the initial position is s (0) = 0: s(t) = How does this compare with the solution to the equation for velocity when there is no air resistance? If c = 0, then v(t) = 19 -9.8t, and if s(0) = 0, then s(t) = 19t – 4.9t. We then have that v(t) = 0 when t = 1.939, and s(1.939) ~ 18.418, and that the positive t solution to s(t) = 0 ist : 3.878, which leads to v(3.878) = -19 meters per second.

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(1 point) A body of mass 7 kg is projected vertically upward with an initial velocity 19 meters per second.
We assume that the forces acting on the body are the force of gravity and a retarding force of air resistance
with direction opposite to the direction of motion and with magnitude clu(t) | where c = 0.5- and v(t) is
the velocity of the ball at time t. The gravitational constant is g = 9.8m/s?.
a) Find a differential equation for the velocity u:
du
dt
-9.8-.5v/7
b) Solve the differential equation in part a) and find a formula for the velocity at any time t:
v(t)
=
Find a formula for the position function at any time t, if the initial position is s (0) = 0:
s(t) =
How does this compare with the solution to the equation for velocity when there is no air resistance?
If c = 0, then v(t) = 19 -9.8t, and if s(0) = 0, then s(t) = 19t – 4.9t.
We then have that v(t) = 0 when t = 1.939, and s(1.939) ~ 18.418,
and that the positive t solution to s(t) = 0 ist : 3.878, which leads to v(3.878) = -19 meters per
second.

 
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