A small cannonball with mass 10 kilograms is shot vertically upward with an initial velocity of 170 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 Assume that k = 0.0025, and use g = - 9.8 meters/second?. Solve the differential equation for the velocity v(t). Don't forget to include the initial condition. v(t) -39200 + 39370e-0.025t x 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) = -39200t – 1574800e-0.025t + 1574800 × Find the maximum height reached by the cannonball. Max height = 14.702 X meters
A small cannonball with mass 10 kilograms is shot vertically upward with an initial velocity of 170 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 Assume that k = 0.0025, and use g = - 9.8 meters/second?. Solve the differential equation for the velocity v(t). Don't forget to include the initial condition. v(t) -39200 + 39370e-0.025t x 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) = -39200t – 1574800e-0.025t + 1574800 × Find the maximum height reached by the cannonball. Max height = 14.702 X meters
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:A small cannonball with mass 10 kilograms is shot vertically upward with an initial velocity of 170
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
Assume that k =
0.0025, and use g =
9.8 meters/second?.
Solve the differential equation for the velocity v(t). Don't forget to include the initial condition.
v(t)
-39200 + 39370e-0.025t x
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)
-39200t – 1574800e-0.025t + 1574800 ×
Find the maximum height reached by the cannonball.
Max height
=| 14.702
X meters
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