Question

You are on an iceboat on frictionless, flat ice; you and the boat have a combined mass M. Along with you are two stones with masses m1 and m2 such that M = 6.0000m1 =12.000m2. To get the boat moving, you throw the stones rearward, either in succession or together, but in each case with a certain speed 17.000 m/s relative to the boat.

a). What is the resulting speed of the boat if you throw the stones simultaneously?

b). What is the resulting speed of the boat if you throw the stones m1 and then m2?

c). What is the resulting speed of the boat if you throw the stones m2 and then m1?

Answer 1

here,

M = 6 * m1 = 12 m2

m1 = 2 * m2

u = - 17 m/s

a)

let the resulting speed of the boat if you throw the stones simultaneously be v

using conservation of momentum

M * v = ( m1 + m2) * u

12 * m2 * v = ( 2 m2 + m2) * 17

solving for v

v = 4.25 m/s

the resulting speed of the boat if you throw the stones simultaneously is 4.25 m/s

b)

let the speed when m1 is thrown be u1

using conservation of momentum

(M + m2 ) * u1 = ( m1) * u

(12 * m2 + m2) * u1 = ( 2 m2) * 17

solving for u1

u1 = 2.62 m/s

let the resulting speed of the boat if you throw the stones m1 and then m2 be v

using conservation of momentum

(M + m2) * u1 = M * v + m2 * u

(12 m2 + m2) * 2.62 =12 m2 * v - m2 * 17

v = 4.25 m/s

the resulting speed of the boat if you throw the stones m1 and then m2 is 4.25 m/s

c)

let the speed when m2 is thrown be u1

using conservation of momentum

(M + m1 ) * u1 = ( m2) * u

(12 * m2 + 2 m2) * u1 = ( m2) * 17

solving for u1

u1 = 0.83 m/s

let the resulting speed of the boat if you throw the stones m2 and then m1 be v

using conservation of momentum

(M + m1) * u1 = M * v + m1 * u

(12 m2 + 2 * m2) * 0.83 = 12 * m2 * v - 2 * m2 * 17

v = 4.25 m/s

the resulting speed of the boat if you throw the stones m2 and then m1 is 4.25 m/s