Question

A firecracker in a coconut blows the coconut into three pieces. Twopieces of equal mass fly off south and west, perpendicular to eachother, at 18 m/s. The third piece has twice the mass asthe other two.Part 1What is the speed of the third piece? (Answer in 2 sig figs andm/s)Part 2What is the direction of the third piece? (Answer in 2 sig figs anddegrees north of east)

Answer 1

1. 13 m/s

2.
`45^(\circ)` north of east

Solution:

As per the question:

Velocity of the two pieces with equal masses, 'm', v = 18 m/s

Mass of the third particle, M = 2m

Now,

To calculate the speed of the third piece

We know that:

Mass 1 flies off to South and mass 2 to West

Now, by the conservation of momentum in the x and y direction:

`Mv'_(y) = mv`

`2mv'_(y) = 18m`

`v'_(y) = 9\ m/s`

Similarly,

`Mv'_(x) = 18m`

`v'_(x) = 9\ m/s`

The resultant velocity of the third piece:

`v' = \sqrt{v'_(x)^(2) + v'_(y)^(2)} = \sqrt{9^(2) + 9^(2)} = 12.73\ m/s` ≈ 13 m/s

Now,

The direction of the third piece can be calculated as:

`tan\theta = (v'_(y))/(v'_(x))`

`\theta = tan^(- 1)((9)/(9)) = 45^(\circ)` in the north of east direction.