An exploding cannonball is initially launched at a speed of 75.0 m/s at an angle

Question

An exploding cannonball is initially launched at a speed of 75.0 m/s at an angle of 30.0 above the horizontal. At its highest point, the cannonball explodes into three pieces. The first piece, with a mass of 2.00 kg, heads straight upward at a speed of 15.0 m/s immediately after the explosion. The second piece, with mass of 2.50 kg, initially moves in the direction 15.0 above the horizontal immediately after the explosion. The third piece, with a mass of 3.00 kg, initially moves in the direction 15.0 below the horizontal immediately after the explosion. (a) How fast do the second and third pieces move immediately after the explosion? (b) How much did the energy of the system increase during the explosion?

Explanation / Answer

Speed at the highest point,

v= v0x = 75 cos30 = 65 m/s

Applying momentum conservation for the explosion,

pi = pf

(2 + 2.50 + 3) (65) i = (2 x 15 j) + (2.50 x v2 (cos15i + sin15j)) + (3 x v3 (cos15i - sin15j))

30 + 2.50 v2 sin15 - 3 v3 sin15 = 0

- 0.647 v2 + 0.776 v3 = 30 ...... (i)

487.5 = 2.415 v2 + 2.90 v3 ..... (ii)

Solving . v2 = 77.7 m/s

v3 = 103.4 m/s

(C) Ki = (2 + 2.50 + 3)(65^2)/2 = 15843.75 J  

Kf = (2 x 15^2 / 2) + (2.50 x 77.7^2 / 2) + (3 x 103.4^2 / 2)

KF = 23809 J  

Energy increase = KF - Ki = 7965 J

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