A boat which has a speed of 5 km h- 1 in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water (in km h- 1 ) is

Question

A boat which has a speed of 5 km h- 1 in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water (in km h- 1 ) is (A) 3 (B) 4 (C) √21 (D) 1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-eiucvxtlhmid.png" /> Speed along the shortest path l⇒| mathrmv mathrmR|=( text distance / text time )=(1/((15)60)) mathrmkm mathrmh-1 ⇒| mathrmv mathrmR|=4 mathrm~km mathrm~h-1 ∴ Speed of water, overset arrow textvwater = √52 - 42 = 3 km h- 1

Q. A boat which has a speed of $5 km h^{- 1}$ in still water crosses a river of width $1 km$ along the shortest possible path in $15$ minutes. The velocity of the river water (in $km h^{- 1}$ ) is

$3$

$4$

$21$

$1$

Speed along the shortest path $l \Rightarrow ∣ ∣ v_{R} ∣ ∣ = \frac{distance}{time} = \frac{1}{( \frac{15}{60} )} km h^{- 1}$
$\Rightarrow ∣ ∣ v_{R} ∣ ∣ = 4 km h^{- 1}$
$∴$ Speed of water, $v \to_{w a t er} = 5^{2} - 4^{2} = 3 km h^{- 1}$

Q. A boat which has a speed of 5kmh−1 in still water crosses a river of width 1km along the shortest possible path in 15 minutes. The velocity of the river water (in kmh−1 ) is

3

4

21​

1

Speed along the shortest path l⇒∣∣​vR​∣∣​= time distance ​=(6015​)1​kmh−1 ⇒∣∣​vR​∣∣​=4 km h−1 ∴ Speed of water, v→water​=52−42​=3kmh−1

Q. A boat which has a speed of $5 km h^{- 1}$ in still water crosses a river of width $1 km$ along the shortest possible path in $15$ minutes. The velocity of the river water (in $km h^{- 1}$ ) is

$3$

$4$

$21$

$1$

Speed along the shortest path $l \Rightarrow ∣ ∣ v_{R} ∣ ∣ = \frac{distance}{time} = \frac{1}{( \frac{15}{60} )} km h^{- 1}$
$\Rightarrow ∣ ∣ v_{R} ∣ ∣ = 4 km h^{- 1}$
$∴$ Speed of water, $v \to_{w a t er} = 5^{2} - 4^{2} = 3 km h^{- 1}$