Vector Question

[hyperblade01]

It seems easy and maybe its just me:

A boat is rowed with a velocity of 5 km/h directly towards the opposite bank of a river that flows at 3 km/h

a) find the velocity of the boat relative to the bank (2 dp)
b) if the river is 500m wide how far down the river will the boat reach the other bank? (to the nearest metre)

[qshyrn]

It seems easy and maybe its just me:

A boat is rowed with a velocity of 5 km/h directly towards the opposite bank of a river that flows at 3 km/h

a) find the velocity of the boat relative to the bank (2 dp)
b) if the river is 500m wide how far down the river will the boat reach the other bank? (to the nearest metre)

asssume water is flowing from left to right
a) magnitude of resultant velocity =SQRT(5^2+3^2)=5.83 km/h
   to get direction:
  find angle the boat goes:  tan-1 (5/3)=59.04 degrees to horizontal, which is (90-59.04)degrees true
b) if 500m wide, we reach the other side in  (0.5/5)hours=0.1hours  (using verticle component)
    we multiply this time with 3km/h  to get distance down the river.  0.1hours x  3km/h =0.3 km
   

[hyperblade01]

I agree with your answers


The reason i was unsure is because in part b) it mentions 'to the nearest metre'. Which could imply the answer wont be neat..and so when i got 300m, i was a bit suspicious