I have a river crossing problem I need help with! I have made the calculation th

Question

I have a river crossing problem I need help with! I have made the calculation that the river is 43.2m wide. I need to find the following answer with calculations.

We will now use vector addition to predict the time to cross, the distance traveled, and the boat speed relative to shore with these inputs: Boat Speed = 6 m/s, angle of launch = 60, and River Speed = 3 m/s. We need to know the velocity of the boat relative to the shore, Vs. This is the vector sum of the velocity of the boat relative to the water, Vb, and the velocity of the water relative to the shore, Vr. This means that Vs = Vb + Vr. To add 2 vectors we need the x and y components of each. Determine the x and y components of these 2 vectors. This is an x and y for Vb and and x and y for Vr. Show all of your work for each part.

Explanation / Answer

bVw = boat's velocity relative to the water
wVg = water's velocity relative to the ground
bVg = boat's velocity relative to the ground

a) Using pythagorean theorem:

(bVg)^2 = (bVw)^2 + (wVg)^2
bVg = ((bVw)^2 + (wVg)^2)
bVg = ((2.60 m/s)^2 + (1.10 m/s)^2)
bVg = 2.82 m/s

b) Position is a vector quantity meaning it has both magnitude and direction. For the magnitude (distance), we know speed is:

v = d / t
d = vt

where:
v= speed
d = distance
t = time

The displacement downstream is:

d = (wVg) t
d = (1.10 m/s) (3.00 s)
d = 3.3 m

The displacement across the river is:

d = (bVw) t
d = (2.60 m/s) (3.00 s)
d = 7.6 m

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.