# A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed with respect to water is 3 km/h. (a) If he heads in a direction making an angle θ with the flow, find the time he takes to cross the river. (b) Find the shortest possible time to cross the river.

Navjyot Kalra
9 years ago
Sol. a) The vertical component 3 sin θ takes him to opposite side. Distance = 0.5 km, velocity = 3 sin θ km/h Time = Distance/(Velocity ) = 0.5/(3 sin⁡θ ) hr = 10/sin θ min. b) Here vertical component of velocity i.e. 3 km/hr takes him to opposite side. Time = Distance/Velocity = 0.5/3 = 0.16 hr ∴ 0.16 hr = 60 x 16 = 9.6 = 10 minute.
rohan duseja
15 Points
4 years ago
the swimmer wont be able to make it only as the speed of river is more as compare to the swimmer
he will drown for sure
ankit singh
3 years ago

## V=3sin∅S=0.5KMT=3sin∅0.5​hours=sin∅10​min​

Vertical componenet to opposite side =3KM/hr
T=30.5=0.16hr=10min
Alex sharma
13 Points
2 years ago
Good afternoon students vha the day dear Tuli the meeting on Google meet at 10 a.m the day of the day dear and I am happy that he is her the most dominant species of which forest and I was eating the food and civil supplies and I was in the form of quadratic equations the day