Home
Class 12
PHYSICS
Estimate the sail area of a sailing boat...

Estimate the sail area of a sailing boat moving at a constant speed in the direction of the wind assuming its midship section to be `S_(0)=1.0 m^(2)`, the coefficient C = 0.1, the boat's speed `v_(0) = 3.0 m//s`, and the wind velocity v =6.0 m/s

Text Solution

Verified by Experts

The correct Answer is:
`5m^(2)`
The problem stipulates that the boat moves over water at a constant speed, and this moans that the drag and the force acting on the sails are equal in magnitude.
To find the formula for the drag of the water compute the Rey- nolds number `Re= p_(0)v_(0)l_(0)//eta_(0)`· It is given that `v_(0) = 3` m/s and that the characteristic dimension is `l_(0) ~~ 1` m. Thus, `Re = 3 xx 10^(6)`, and so the pressure drag `R = CS_(0)P_(0)v_(0)^(2)//2` plays a basic role.
To be definite let us assume that the interaction of the air with the sails is elastic. Noting also that nm= p is the density of air, we obtain `1/2CS_(0)p_(0)v_(0)^(2)=2psv^(2)`. The area of the sails is
`S=(CS_(0)p_(0)v_(0)^(2))/(4pv^(3))=(0.1xx1.0xx10^(3)x9.0)/(4xx1.3xx36.0)=5m^(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A boy (mass of 40 kg) is standing at one end of a boat (mass of 60 kg) in still water. The length of the boat is 10 m and the boy takes 2s to reach at other end of boat moving with constant speed. Assuming no friction between the boat and the water. (i) The distance covered by the boat is 4 m (ii) The distance covered by the boy with respect to the ground is 6 m . (iii) The velocity of the boy with respect to the ground is lt 5 m//s (iv) The velocity of the boy is 3 m//s

A 3.0-kg cart moving to the right with a speed of 1.0 m/s has a head-on collision with a 5.0-kg cart that is initially moving to the left with a speed of 2.0 m/s. After the collision, the 3.0-kg cart is moving to the left with a speed of 1.0 m/s. What is the final velocity of the 5.0-kg cart?

A 400 m wide river is flowing from west to east at velocity 3m/s. A boat starts from one bank and it crosses the river along the shortest path. When it reaches the middle of river, wind starts blowing horizontally along north-east at a velocity sqrt(2) m/s . Due to this, the direction of rowing of boat has to be changed for the boat to move along the shortest path. If the velocity of boat in still water with no wind blowing is 5 m/s, then choose the correct option(s).

The speed of a moving object is determined to be 0.06 m/s. This speed is equal to :

Two boats A and B are moving along perpendicular paths in a still lake at night. Boat A move with a speed of 3 m//s and boat B moves with a speed of 4 m//s in the direction such that they collide after sometime. At t=0 , the boats are 300 m apart. The ratio of distance of distance travelled by boat A to the distance travelled by boat B at the instant of collision is :-

A person moves due east at speed 10 m/s and feels the wind is blowing towards south at speed 10 m/s. Find actual velocity of wind flow -

A 0.1 kg body moves at a constant speed of 10 m/s. It is pushed by applying a constant force for 2 s. Due to this force, it starts moving exactly in the opposite direction with a speed of 4 m//s . Then

Twp boats are moving along perpendicular paths on a still take at right. One boat moves with a speed of 3 ms^(-1) and the other boat moves with a speed of 4 ms^(-1) in the directions such that they collide after some time. At t=0, the boats are 300 m apart. Two boats will collide after time ______.

The speed of a moving object is determined to be 0.06 m//s . This speed is equal to :