Part of JME-01 — Kinematics: Rectilinear & Projectile Motion

Projectile on Inclined Plane

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For projectile on a plane inclined at angle alpha:

Set axes along and perpendicular to the incline:

  • Along incline: axa_x' = -g*sin(alpha) [deceleration going up]
  • Perpendicular to incline: aya_y' = -g*cos(alpha)

If launched at angle beta to the incline with speed u:

  • uxu_x' = ucos(beta), uyu_y' = usin(beta)
  • Time of flight: T = 2u*sinbeta(gcos(alpha)\frac{beta}{(g*cos(alpha)})
  • Range along incline: R = 2u2u^2*sin(beta)*cosalpha+beta(gcos2(alpha)\frac{alpha+beta}{(g*cos^2(alpha)})
  • Max range when beta = (pi/4 - alpha/2), i.e., bisect angle between incline and vertical

JEE trick: Range up the incline != range down the incline for the same launch angle.

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