A small cannonball with mass 4 kilograms is shot vertically upward with an initial velocity of 190 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 mg - kv dt Assume that k = 0.0025, and use g = -9.8 meters/second². Solve the differential equation for the velocity v(t). Don't forget to include the initial condition. v(t) = = 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 = meters
A small cannonball with mass 4 kilograms is shot vertically upward with an initial velocity of 190 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 mg - kv dt Assume that k = 0.0025, and use g = -9.8 meters/second². Solve the differential equation for the velocity v(t). Don't forget to include the initial condition. v(t) = = 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 = meters
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:A small cannonball with mass 4 kilograms is shot vertically
upward with an initial velocity of 190 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
mg - kv
dt
Assume that k
=
0.0025, and use g =
-9.8
meters/second².
Solve the differential equation for the velocity v(t). Don't
forget to include the initial condition.
v(t) =
=
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 =
meters
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
