Question

Two iceboats hold a race on a frictionless horizontal lake. The two iceboats have masses m and 2m. Each iceboat has an identical sail, so the wind exerts the same constant force F on each iceboat. The two boats start from rest and cross the finish line a distance s away. Which iceboat crosses the finish line with greater momentum?


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Answer 1

Answer:

the 2nd boat with the 2m will cross the finish line with greater momentum

Answer 2

Answer:

Mass m Iceboat crosses the finish line with greater momentum.

Explanation:

Since the force acting on the boats is constant (F) so we can use the equations of motion.

Since F=ma

⇒a=F/m

Acceleration of iceboat with(mass m) is,

$a_{1} =\frac{F}{m}$

Acceleration of iceboat( mass 2m) is,

$a_{2} =\frac{F}{2m}$

Final velocity of the boats can be given by the third equation of motion,

                                                v²=u²+2as

Since initial velocity of both the iceboats is 0(They start from rest),

so final velocity is given by $v=\sqrt{2as}$

Final velocity of iceboat(mass m) is,

$v_{1} =\sqrt{2\frac{F}{m}s }$

Final velocity of iceboat( mass 2m) is,

$v_{2} =\sqrt{2\frac{F}{2m}s }$

Final momentum of iceboat (mass m) is,

$p_{1} =m_{1} v_{1} =m\sqrt{2\frac{F}{m}s }=\sqrt{2Fms} Kgm/s$

Final momentum of iceboat(mass 2m) is,

$p_{2} =m_{2} v_{2} =m\sqrt{2\frac{F}2{m}s }=\sqrt{Fms} Kgm/s$

Since $p_{1} > p_{2}$ ,

Mass m Iceboat crosses the finish line with greater momentum.