A small cannonball with mass 4 kilograms is shot vertically upward with an initial velocity of 110 meters per second. If the air resistance is assumed to be directly proportional to the speed of the cannonball, a differential equation modeling the projectile velocity is m dv dt mg kv. 9.8 meters/second². Solve the differential equation for the velocity v(t). Don't forget to include the initial condition. v(t) = = Assume that k = 0.0025, and use g =
A small cannonball with mass 4 kilograms is shot vertically upward with an initial velocity of 110 meters per second. If the air resistance is assumed to be directly proportional to the speed of the cannonball, a differential equation modeling the projectile velocity is m dv dt mg kv. 9.8 meters/second². Solve the differential equation for the velocity v(t). Don't forget to include the initial condition. v(t) = = Assume that k = 0.0025, and use g =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need only handwritten solution only (not typed one).
![A small cannonball with mass 4 kilograms is shot vertically upward with an initial velocity of
110 meters per second. If the air resistance is assumed to be directly proportional to the
speed of the cannonball, a differential equation modeling the projectile velocity is
dv
m. = mg - kv.
dt
9.8 meters/second².
Solve the differential equation for the velocity v(t). Don't forget to include the initial
condition.
Assume that k
v(t)
=
=
=
0.0025, and use g
-
Integrate the velocity to obtain the height h(t) as a function of time. Assume the cannonball
is launched from ground level at t = = 0.
h(t):
Find the maximum height reached by the cannonball.
Max height =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2646fcad-9187-4f77-a9b4-e1a52a127411%2Fd52c7540-4668-4bdf-aed0-8e7216c929be%2F3t3iifb_processed.png&w=3840&q=75)
Transcribed Image Text:A small cannonball with mass 4 kilograms is shot vertically upward with an initial velocity of
110 meters per second. If the air resistance is assumed to be directly proportional to the
speed of the cannonball, a differential equation modeling the projectile velocity is
dv
m. = mg - kv.
dt
9.8 meters/second².
Solve the differential equation for the velocity v(t). Don't forget to include the initial
condition.
Assume that k
v(t)
=
=
=
0.0025, and use g
-
Integrate the velocity to obtain the height h(t) as a function of time. Assume the cannonball
is launched from ground level at t = = 0.
h(t):
Find the maximum height reached by the cannonball.
Max height =
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