A swimmer, capable of swimming at a speed of 1.97 m/s in still water (i.e., the swimmer can swim with a speed of 1.97 m/s relative to the water), starts to swim directly across a 2.77-km-wide river. However, the current is 1.13 m/s, and it carries the swimmer downstream. (a) How long does it take the swimmer to cross the river? (b) How far downstream will the swimmer be upon reaching the other side of the river?
20s
Tan A = Y/X = 1.97/1.13.
A = 60.2o N. of E.
Vr = 1.97/sin60.2=2.27 m/s.= Resultant
velocity.
Sin 60.2 = 2.77/d.
d = 2.77/sin60.2 = 3.19 km. = Distance
traveled to cross.
a. d = Vr*t = 3190 m.
2.27*t = 3190.
t = 1405 s. = 23.4 Min.
b. d = 3.19*Cos60.2 = 1.58 km.
To solve this problem, we can use the concept of vector addition. We'll break the swimmer's velocity into two components: one perpendicular to the river's flow and the other parallel to the river's flow.
Let's tackle each question step by step:
(a) To find how long it takes the swimmer to cross the river, we need to determine the swimmer's cross-river velocity. This is the component of the swimmer's velocity that is perpendicular to the river's flow.
The cross-river velocity can be found using the Pythagorean theorem:
cross-river velocity = √(swimmer velocity^2 - river velocity^2)
cross-river velocity = √(1.97 m/s)^2 - (1.13 m/s)^2
Calculate the cross-river velocity using the formula:
cross-river velocity = √(1.97^2 - 1.13^2) m/s
Once you've calculated the cross-river velocity, you can find the time it takes to cross the river using the formula:
time = distance / cross-river velocity
In this case, the distance is 2.77 km. Make sure to convert it to meters by multiplying by 1000:
time = (2.77 km * 1000 m/km) / cross-river velocity
Calculate the time using the formula.
(b) To find how far downstream the swimmer will be upon reaching the other side of the river, we need to determine the swimmer's downstream velocity. This is the component of the swimmer's velocity that is parallel to the river's flow.
The downstream velocity is equal to the river's velocity, which is 1.13 m/s. Since the swimmer is carried downstream by the current, this is the distance the swimmer will be downstream.
Now that we've explained the steps, you can perform the calculations and find the answers for (a) and (b).