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An arrow is shot straight upward from the ground with an initial velocity of 10 ms4. The air resistance is equal to ku g, where v is the velocity of the arrow, k is a constant and g is the gravitational constant. The differential equation is given by dv dr where z is the displacement of the arrow at time t which is taken as positive in the upward direction. Given that g = 9.8 ms-2 and -kv – 9. k = 0.05, i. Find the expression of the motion in terms of v and r. ii. Find the maximum height attained by the arrow. UTM UTM

An arrow is shot straight upward from the ground with an initial velocity of 10 ms4. The air resistance is equal to ku g, where v is the velocity of the arrow, k is a constant and g is the gravitational constant. The differential equation is given by dv dr where z is the displacement of the arrow at time t which is taken as positive in the upward direction. Given that g = 9.8 ms-2 and -kv – 9. k = 0.05, i. Find the expression of the motion in terms of v and r. ii. Find the maximum height attained by the arrow. UTM UTM

Advanced Engineering Mathematics
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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b) An arrow is shot straight upward from the ground with an initial velocity of 10 ms-1, The air resistance is equal to ku g, where v is the velocity of the arrow, k is a constant and g is the gravitational constant. The differential equation is given by SUTM dv -ku – 9. dz where r is the displacement of the arrow at time t which is taken as %3! UTMUTM positive in the upward direction. Given that g = 9.8 ms-² and UTM k = 0.05, TM i. Find the expression of the motion in terms of v and r. ii. Find the maximum height attained by the arrow. SUTMUTM XUTM UTM UTM UTMUTM UTM
Transcribed Image Text:b) An arrow is shot straight upward from the ground with an initial velocity of 10 ms-1, The air resistance is equal to ku g, where v is the velocity of the arrow, k is a constant and g is the gravitational constant. The differential equation is given by SUTM dv -ku – 9. dz where r is the displacement of the arrow at time t which is taken as %3! UTMUTM positive in the upward direction. Given that g = 9.8 ms-² and UTM k = 0.05, TM i. Find the expression of the motion in terms of v and r. ii. Find the maximum height attained by the arrow. SUTMUTM XUTM UTM UTM UTMUTM UTM
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