Home
Class 11
PHYSICS
An aeroplane is flying with velocity ve...

An aeroplane is flying with velocity ` vec v_p = 100 ms^(-1)` towards East
with respect to ground through motionless air and ` vec v_w` is the wind velocity with respect of ground. The total velocity of aeroplane is ` vec v=vec v_P+ vec v_w`
The magnitude of the velocity is often called speed . the heading of the plane is the direction in which the nose of the plane points. In fact, it is the direction in which the engine propels the plane . Answer the following questions :
If ` theta` is the answer to question ` 15 6`, the total speed of the plane in ` ms^(-1)` is.

A

` 100 sin theta`

B

` 100 cos theta`

C

` 100 cosec theta `

D

`100 sec theta`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, ` tan theta = (25)/(100) = 1/4` ,
` cos theta 4/(sqrt( 4^2 +1^2) = 4/(sqrt17)`
Resultant speed of the plane,
` v= sqrt (v_P^2 +v_w^2) = sqrt ( 100^2 + 25^@)`
`= sqrt (25^2 +4^2 25^2) = 25 sqrt 17 ms^(-1)`
:.` v = (25 sqrt 17)/(cos theta) xx cos theta = (25sqrt17)/( cos theta) xx 4/(sqrt 170 = ( 100)/(cos theta)`.
Promotional Banner

Topper's Solved these Questions

  • KINEMATICS

    PRADEEP|Exercise 4 NCERT Integer type|4 Videos

  • KINEMATICS

    PRADEEP|Exercise 1 NCERT Assertion-Reaseon Type|14 Videos

  • KINEMATICS

    PRADEEP|Exercise 3 NCERT multiple|161 Videos

  • GRAVIATION

    PRADEEP|Exercise Assertion-Reason Type Questions|19 Videos

  • LAWS OF MOTION

    PRADEEP|Exercise Assertion- Reason Type Questions|17 Videos

Similar Questions

Explore conceptually related problems

An aeroplane is fluisg with velocity vec v_p (= 100 ms^(-1) towards East) with respect to ground through motionless air and vec v_w is the wind velocity with respect ot ground. The total velocity of aeroplane is vec v=vec v_P+ vec v_w The magnitude of the velocity is often called speed . the heading of the plane is the direction in which the nose of the plane is the direction is which th nose fo the plane points. In fact, it is the direction in which the engine propels the plane . Abswer the following questions : If the wind blow with velocity 25 ms^(-1) Norhtwards, the plane velocity is deflected from East by an angle.

A car is moving with velocity vec v_(c) towards north and a train is moving towards east with velocity vec v_(t) . Find the direction of relative velocity of car with respect to train.

An aeroplane is flying with the velocity of V_(1)=800kmph relative to the air towards south.A wind with velocity of V_(2)=15ms^(-1) is blowing from west to east.What is the velocity of the aeroplane with respect of the earth.

The linear velocity of a particle on a rotating body is given by vec v = vec omega xx vec r" where "vec omega is the angular velocity and vec r is the radius vector. What is the value of |v| if vec omega = hati -2hatj+2hatk and vec r =4hatj-3hatk ?

Let vec u and vec v be unit vectors such that vec u xxvec v+vec u=vec w and vec w xxvec u=vec v. Find the value of [vec uvec vvec w]

A particle moving in the xy plane experiences a velocity dependent force vec F = k (v_yhati + v_x hat j) , where v_x and v_y are the x and y components of its velocity vec v . If vec a is the acceleration of the particle, then which of the following statements is true for the particle?

An electron is launched with velocity vec v in a uniform magnetic field vec B. The angle theta between vec v and vec B lies between 0 and pi /2 . Its velocity vector vec v returns to its initial value in a time interval of

If vec a, vec b, vec c are non-coplanar vectors and vec v * vec a = vec v * vec b = vec v * vec c = 0, then vec v must be a

A particle of mass m moves in the xy-plane with velocity of vec v = v_x hat i+ v_y hat j . When its position vector is vec r = x vec i + y vec j , the angular momentum of the particle about the origin is.