Home
Class 11
PHYSICS
A bird moves with velocity 20m s^(-1) in...

A bird moves with velocity `20m s^(-1)` in a direction making an angle of `60^(@)` with vertical upward .Represent the velocity vector in a rectangular form.

Text Solution

Verified by Experts

Let the easten line be taken as x-axis ,northen as y-axis,and vertical upward as z-axis . Let the velocity`v` makes angles `alpha, beta`, and `gamma` with x-, y- and z-axis, respectively. Then `alpha=60^(@)` and `gamma=60^(@)`.
`cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1`
We have `cos^(2)60^(@)+cos^(2)beta+cos^(2)60^(@)=1`
or `cos beta=1/sqrt(2)`
` vec(v)=vcos alpha hat(i)+v cos beta hat (j)+v cos gamma hat(k)`
`=20[1/2hat(i)+1/sqrt(2)hat(j)+1/2hat(k)]=10hat(i)+10sqrt(2)hat(j)+10hat(k)`
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    CENGAGE PHYSICS|Exercise Exercise 3.1|19 Videos

  • VECTORS

    CENGAGE PHYSICS|Exercise Exercise 3.2|13 Videos

  • TRAVELLING WAVES

    CENGAGE PHYSICS|Exercise Integer|9 Videos

  • WORK, POWER & ENERGY

    CENGAGE PHYSICS|Exercise Archives (integer)|4 Videos

Similar Questions

Explore conceptually related problems

A bird is moving with velocity 10 ms?^(-1) in a direction making an angle of 60^@ with vertical upward. Represent the velocity vector in rectangular form.

A bird moves with velocity 20m/s in a direction making an angle of 60^(@) with the eastern line and 60^(@) with the vertical upward. Represent the velocity vector in rectangular form.

A bird ,moves with velociry 20 m/ s in a direction making an, :angle of 60^(@) with the eastern line and 60^(@) with verticalj lupward~present the velocity vector in rectan!(Ular form.

A bird moves with velocity 10 ms^(-1) in a direction making an angle if 60 ^@ with the eastern derction and 45^@ with vertical upward direction. Represent the velocity vector of bird in rectanular form.

A body is projected with a velocity of 20 ms^(-1) in a direction making an angle of 60^(@) with the horizontal. Determine its (i) position after 0.5 s and (ii) the velocity after 0.5s .

A particle is projected with an initial velocity of 200 m//s in a direction making an angle of 30^(@) with the vertical. The horizontal distance covered by the particle in 3s is