Physics # The projection of a particle on to a inclined plane is shown in the figure. ‘B’ is the point at which velocity is parallel to inclined plane. Identify the correct options of the following. (t1, t2 are time intervals for the journey AB, BC respectively and V1, V2, V3, V4 are components of velocities along inclined plane, perpendicular to inclined plane)​

For particle projected up the plane, in this situation we take two axes , one perpendicular to the plane and other along the plane then , taking component of velocity and acceleration along these axes we get :

along x-axis u

x

=10cos30

0

=5

3

,a

x

=−gsin30

0

=−5

and along y-axis, u

y

=10sin30

0

=5,a

y

=−gcos30

0

=−5

3

using these we get, time of flight T=

a

y

2u

y

=

5

3

2×5

=

3

2

so, v

x

=u

x

+a

x

t=5

3

−5×

3

2

=

3

5

3

m/s

and v

y

=u

y

+a

y

t=5−5

3

×

3

2

=−5m/s

so speed with which particle strike the inclined will be v=

(

v

x

2

+v

x

2

)=

(

25/3+25)=

3

10

m/s

and component of velocity perpendicular to the plane when it strikes at A is 5m/s

467 