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

Answer

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

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

$V_3 = \dfrac{V}{3}(-\hat{i}-\hat{j})$

$V_3 = \dfrac{V}{3}\sqrt{1^2+1^2}$

$V_3 = \dfrac{V}{3}\sqrt{2}$

velocity of third component

$V_3 = \dfrac{31}{3}\sqrt{2}$

$V_3 = 14.61\ m/s$

angle

$\theta = tan^{-1}(\dfrac{-1}{-1})$

$\theta = tan^{-1}(1)$

$\theta = 45^0$