Year 12 Maths Extension 2 (2027)
Mechanics
Projectiles in Resisted Motion
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Questions
Question 1
183627
A projectile is fired from the origin with speed \(u\) at angle \(\theta\) to the horizontal, in a medium whose resistance produces a retardation of \(k\) times the velocity. Taking \(x\) horizontal, show that the horizontal velocity is \(\dot{x} = u\cos\theta\, e^{-kt}\).
x-ddot=-k x-dot; with w=x-dot, dw/dt=-kw; ln w=-kt+C; w=u cos th at t=0 -> x-dot = u cos th e^-kt.
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