posted by Jack Hill .
A 4.0 x 101 kg wind sled is gliding East across a frozen lake at a constant speed of 12 m/s, when a gust of wind from the southwest exerts a constant force of 1.0 x 102 N on its sails for 3.0 s. With what velocity will the sled be moving after the wind has subsided?
p=mv=40•12 =480 kg•m/s.
Impulse = F•Δt=100•3=300 kg•m/s.
p is directed to the East
F•Δt=p1 is directed to the northeast.
p and p1 make the angle α=45º
Another angle in the parallelogram of momenta is [360-(2•45)]/2=135º
Use cosine law
p(net) =sqrt(p²+p1²-2p•p1•cos α) =
=sqrt(480²+ 300² -2•480•300•cos 135º)=
=sqrt(480²+ 300² +2•480•300•0.707)= 723.9 kg•m/s.
v=p(net)/m =723.9/40=18.1 m/s