Question

Super Urgent Plz HELP! A swimmer has a swimming speed of 5.35 m/s in still water. When she heads directly across the river, she ends up travelling downstream at an angle of 30° (with respect to a line perpendicular to the shore). (a) What is the speed of the current? (b) What heading would the boat need to have in order to reach a point directly across the river? (c) If the stream is 15 m wide, how long would a trip directly across the river take?

Answer 1

(a)3.09 m/sec (b)θ= 35.28° (c) t =3.43 sec

Step-by-step explanation:

Solution

Given that:

The swimming speed of swimmer =5.35 m/s

The downstream angle = 30°

Now,

(a)we find speed of the current which is given below:

V = V swimmer + V river

Tan 30° = Vr/Vs

Thus

Vr = 5.35 * tan 30°

Vr = 5.35 * 0.5773

= 3.09 m/sec

(b)She would have velocity at direction such that she reaches across the shore

Then

Vs sin θ =Vr

sin θ = Vs/Vr

sin θ = 3.09/5.35

θ= 35.28°

Therefore, She had to make θ= 35.28° on another side of the river

(c) Thus

t = d/Vs cosθ

=15/5.35 * cos (35.28°)

t =3.43 sec