Let the width of the river be \( d \).
Case 1: Shortest Path To cross the river along the shortest path (perpendicular to the river flow), the boat must counteract the river's flow. The effective velocity of the boat perpendicular to the river flow is: \[ V_{{eff}} = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12 \, {ms}^{-1} \] The time taken to cross the river along the shortest path is: \[ t_1 = \frac{d}{12} \] Case 2: Shortest Time To cross the river in the shortest time, the boat should head directly across the river (perpendicular to the flow) without counteracting the flow. The effective velocity of the boat is simply its velocity in still water: \[ V_{{eff}} = 13 \, {ms}^{-1} \] The time taken to cross the river in the shortest time is: \[ t_2 = \frac{d}{13} \] Ratio of Times The ratio of the times taken is: \[ \frac{t_1}{t_2} = \frac{\frac{d}{12}}{\frac{d}{13}} = \frac{13}{12} \] Thus, the ratio is 13:12.
Final Answer: 13:12
A uniform circular disc of radius \( R \) and mass \( M \) is rotating about an axis perpendicular to its plane and passing through its center. A small circular part of radius \( R/2 \) is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.
A metal rod of 50 cm length is clamped at its midpoint and is set to vibrations. The density of that metal is \( 2 \times 10^3 \, {kg/m}^3 \).
Young's modulus of that metal is \( 8 \times 10^8 \, {Nm}^2 \). The fundamental frequency of the vibration is
Two statements are given below
Statement I: Benzanamine can be prepared from phthalimide.
Statement II: Benzanamine is less basic than phenyl methanamine.
What are X and Z in the following reaction sequence?
What is Y in the following reaction sequence?
Observe the following set of reactions:
Correct statement regarding Y and B is:
What is X in the following reaction?