Consider a sraight river whose course is directly in line with the west-east dir
ID: 1332415 • Letter: C
Question
Consider a sraight river whose course is directly in line with the west-east direction. The north-south distance acrosee the river from bank to bank is y=88.0m. The river's watercurrent flows due east at a velocity relative to the ground of v=5.00 m/s. A boat pointed due north begins to cross the river from the south bank with a velocity relative to the water of v=3.30 m/s. By the time it crosses the river and reaches the north shore, the river current has taken the boat a distance x to the east, so the boat relative to the ground traveled east of north at an angle theta measured from due north.
1) Determine the time interval required for the boat to travel from its starting point on the south shore to its ending point on the north shore.
2) Determine the distance x described above.
3) Determine the velocity of the boat relative to the ground expressing your result in unit-vector notation.
4) Determine the magnitude of the velocity of the boat relative to the ground and its direction angle as measured from due north.
Explanation / Answer
velocity of boat relativ eto groung = 5i + 3.3j
(a)
time taken = t = y/vy = 88/3.3 = 26.7 s
(b)
x = vx*t = 5*26.7 = 133.5 m
(c)
v =5i + 3. j
d)
V = sqrt(5^2+3.3^2) = 6 m/s
direction = tan^-1(vx/vy) = tan^-1(5/3.3) = 56.6 from north