We know that when a boat travels in water, its net velocity w.r.t. ground is the vector sum of two velocities. First is the velocity of boat itself in river and other is the velocity of water w.r.t. ground. Mathematically:

`vecv_(boat) = vecv_(boat,water) + vecv_(water)`.
Now given that velocity of water w.r.t. ground in a river is u. Width of the river is d.
A boat starting from rest aims perpendicular to the river with an acceleration of a = 5t, where t is time. The boat starts from point (1,0) of the coordinate system as shown in figure. Assume SI units.

Options

A. `(3d//5)^(1//3)`
B. `(6d//5)^(1//3)`
C. `(6d//5)^(1//2)`
D. `(2d//3)^(1//3)`

Answer

B

Explanation

b. `a = 5t rArr (dv_y)/(dt) = 5t rArr v_y = (5t^2)/2`
`rArr (dy)/(dt) = 5/2 t^2 rArr y = 5/6 t^3`
Putting ` y = d, we get d = 5/2 t^3 rArr t = ((6d)/5)^(1//3)`.