Question:
A man crosses a 320 m wide river perpendicular to the current in 4 min. If in still water he can swim with a speed 5/3 times that of the current, then the speed of the current, in m/min is
A man crosses a 320 m wide river perpendicular to the current in 4 min. If in still water he can swim with a speed 5/3 times that of the current, then the speed of the current, in m/min is
Show Hint
To cross river perpendicularly, swimmer must head upstream at angle \(\theta = \sin^{-1}(v_r/v_m)\).
Updated On: Apr 23, 2026
- 30
- 40
- 50
- 60
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Resultant velocity across river = width/time. Also, \(v_m = \frac{5}{3}v_r\).
Step 2: Detailed Explanation:
Width = 320 m, time = 4 min. Velocity across river = \(\frac{320}{4} = 80\) m/min.
Let current speed = \(v_r\). Man's speed in still water = \(\frac{5}{3}v_r\).
To cross perpendicularly, \(v_m^2 = v_r^2 + (80)^2\) (vector addition: man swims at angle upstream).
\(\left(\frac{5}{3}v_r\right)^2 = v_r^2 + 6400 \Rightarrow \frac{25}{9}v_r^2 = v_r^2 + 6400 \Rightarrow \frac{16}{9}v_r^2 = 6400\).
\(v_r^2 = 6400 \times \frac{9}{16} = 400 \times 9 = 3600 \Rightarrow v_r = 60\) m/min.
Step 3: Final Answer:
Thus, speed of current = 60 m/min.
Resultant velocity across river = width/time. Also, \(v_m = \frac{5}{3}v_r\).
Step 2: Detailed Explanation:
Width = 320 m, time = 4 min. Velocity across river = \(\frac{320}{4} = 80\) m/min.
Let current speed = \(v_r\). Man's speed in still water = \(\frac{5}{3}v_r\).
To cross perpendicularly, \(v_m^2 = v_r^2 + (80)^2\) (vector addition: man swims at angle upstream).
\(\left(\frac{5}{3}v_r\right)^2 = v_r^2 + 6400 \Rightarrow \frac{25}{9}v_r^2 = v_r^2 + 6400 \Rightarrow \frac{16}{9}v_r^2 = 6400\).
\(v_r^2 = 6400 \times \frac{9}{16} = 400 \times 9 = 3600 \Rightarrow v_r = 60\) m/min.
Step 3: Final Answer:
Thus, speed of current = 60 m/min.
Was this answer helpful?
0
0
Top MET Physics Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- A rope of mass $0.1\, kg$ is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At [he contact point between the rope and the wall, the rope makes an angle $ \theta =10^{\circ} $ with respect to horizontal. The tension in the rope at its midpoint between the walls is
- At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as
View More Questions
Top MET band theory of solids Questions
- The majority charge carriers in a p-type semiconductor are:
- There are 20 naturally occurring amino acids. The maximum number of tripeptides that can be obtained is
- The energy required to break the covalent bond in a semiconductor is:
- Who said, “Number of transistors per square inch on integrated circuits double every year…”?
- The energy gap between the valence and conduction bands of an insulator is about:
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions