A projectile of mass 0.736 kg is shot from a cannon, at height 7 m, as shown in

Question

A projectile of mass 0.736 kg is shot from a cannon, at height 7 m, as shown in the figure, with an initial velocity v1 having a horizontal component of 5.3 m/s. The projectile rises to a maximum height of 4 m above the end of the cannon?s barrel and strikes the ground a horizontal distance ?x past the end of the cannon?s barrel. a.) Find the magnitude of the initial vertical velocity vector of the cannon-ball at the end of the cannon?s barrel. The acceleration of gravity is 9.8 m/s2 . b.) Find the work done by the gravitational force on the particle during its trajectory from the end of the cannon?s barrel to its impact on the ground. Answer in units of J. c.) Find the magnitude of the final velocity vector when the particle impacts the ground.

Explanation / Answer

a) vix = 5.3 m/s, viy = vixtan(59) = 8.8 m/s vi = (5.3 m/s) i+ (8.8 m/s) j b) work W = mgh = 0.736g * 7 m = 50.5 J c) W = mv2/2 - mvi2/2 note vx = vix W = m(vy2 - viy2)/2 vy = (viy2 + 2W/m) =14.7 m/s v = (5.3 m/s) i + (14.7 m/s)j magnitude = 15.6 m/s

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