1. What is v x , the x-component of the swimmer\'s velocity with respect to the

Question

1.

What is vx, the x-component of the swimmer's velocity with respect to the ground?

a. vx=v1sin??v2

b. vx=v1cos??v2

c. vx=v2?v1sin?

d. vx=v2?v1cos?

e. vx=v2cos??v1cos?

f. vx=v2sin??v1sin?

2. What is vy, the y-component of the swimmer's velocity with respect to the ground?

vy=v1sin?

vy=v1cos?

vy=v2cos??v1cos?

vy=v2sin??v1sin?

vy=?v1cos?

vy=?v1sin?

3. Given that the magnitudes of v1 = 6.25 m/s, v2 = 2.5 m/s, and ?= 30o, what is the speed of the swimmer with respect to the ground?

v = 6.73 m/s

v = 8.75 m/s

v = 3.75 m/s

v = 5.45 m/s

v = 4.27 m/s

v = 7.94 m/s

4. If v2 (the speed of the river) is decreased, keeping all other parameters the same, how does the final speed of the swimmer with respect to the ground change?

v increases.

v stays the same.

v decreases.

Explanation / Answer

1.
What is vx, the x-component of the swimmer's velocity with respect to the ground?
a. vx=v1sinv2
b. vx=v1cosv2
c. vx=v2v1sin
d. vx=v2v1cos
e. vx=v2cosv1cos
f. vx=v2sinv1sin

Let vx be the velocity of swimmer wrt the ground.
Now,
vx = Celocity of swimmer wrt water + velocity of current
vx = - v1sin + V2
vx = v2v1sin

2. What is vy, the y-component of the swimmer's velocity with respect to the ground?
vy=v1sin
vy=v1cos
vy=v2cosv1cos
vy=v2sinv1sin
vy=v1cos
vy=v1sin

Let vx be the velocity of swimmer wrt the ground.
Now,
vx = Celocity of swimmer wrt water + velocity of current
vx = v1cos + 0
vx = v1cos

3. Given that the magnitudes of v1 = 6.25 m/s, v2 = 2.5 m/s, and = 30o, what is the speed of the swimmer with respect to the ground?
v = 6.73 m/s
v = 8.75 m/s
v = 3.75 m/s
v = 5.45 m/s
v = 4.27 m/s
v = 7.94 m/s

vx = v2v1sin
vx = 2.5 - 6.25*sin30 = -0.625 m/s

vy = v1cos
vy = 6.25cos30 = 5.412

v = (-0.625^2 + 5.412^2)^1/2
v = 5.45 m/s

4. If v2 (the speed of the river) is decreased, keeping all other parameters the same, how does the final speed of the swimmer with respect to the ground change?
v increases.
v stays the same.
v decreases.

If v2 decreases then

vx = v2v1sin
Hence
Vx decreases (since the value is negative)
vx^2 increases (becomes positive)
Hence V increases

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