Question

A watermelon is blown into three pieces by a large firecracker. Two pieces of equal mass m fly away perpendicular to one another, one in the x direction another in the y direction. Both of these pieces fly away with a speed of V = 31 m/s. The third piece has three times the mass of the other two pieces.

Answer 1

given,

watermelon blown into three pieces

two pieces of mass m

both pieces speed = v = 31 m/s

mass of third piece = 3 m

using conservation of mass

`0 = m V \hat{i} + m V \hat{j} + (3\ m)V_3`

`V_3 = (V)/(3)(-\hat{i}-\hat{j})`

`V_3 = (V)/(3)√(1^2+1^2)`

`V_3 = (V)/(3)√(2)`

velocity of third component

`V_3 = (31)/(3)√(2)`

`V_3 = 14.61\ m/s`

angle

`\theta = tan^(-1)((-1)/(-1))`

`\theta = tan^(-1)(1)`

`\theta = 45^0`