The boat must cross a river with a width of L = 35 m and with a current speed of u = 07 m / s so as to moor

The boat must cross a river with a width of L = 35 m and with a current speed of u = 07 m / s so as to moor exactly opposite the place of departure. It can move at different speeds, while the travel time, measured in seconds, is determined by the expression t = L / U ctg, where is an acute angle that sets the direction of its movement (measured from the coast). What is the minimum angle (in degrees) you need to swim so that the travel time is no more than 50 s?

1. Given:

L = 35 m – width of the river;
u = 7 m / s – boat speed;
t = L / u * ctgφ – travel time;
φ is the angle that sets the direction of its movement, measured from the coast;
tmax = 50 s;
φmin =?
2. For a given constraint, the following inequality must be satisfied:

t ≤ tmax;
L / u * ctgφ ≤ tmax;
ctgφ ≤ tmax / (L / u).
3. Substitute the values of the variables and find the minimum value of the angle:

ctgφ ≤ 50 / (35/7);
ctgφ ≤ 50/5;
ctgφ ≤ 10;
φ ≥ arcctg (10), (the cotangent decreases on the interval (0; π / 2));
φ ≥ 5.7 °;
φmin = 5.7 °.
Answer: at an angle of 5.7 °.