A small ball is projected up a smooth inclined plane with initial speed of 10m/s along the direction at #30 ^@# to the bottom edge of the slope. It returns to the edge after 2 sec. The ball is in contact with the inclined plane throughout the process.?

Question

What is the inclination of the inclined plane?

Ans : #30^@#

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Answer 1 · 2017-08-30T15:30:19

drawn

the velocity of projection of the ball on the inclined floor #u=10m"/"s#
the angle of projection with the bottom edge of the slope #alpha=30^@#
The effective acceleration due to gravity towards the bottom edge will be #gsintheta#, considering the angle of inclination of the slope is #theta# and acceleration due to gravity #g=10m"/"s^2#
The net displacement of the ball along the normal to the bottom edge of the inclined plane during its motion of #t=2 sec# on the inclined floor is zero .
Hence by applying equation of kinematics we can write

#0=usin30^@xxt-1/2gsinthetaxxt^2#

#=>0=10sin30^@xx2-1/2xx10sinthetaxx2^2#

#=>sintheta=sin30^@#

#=>theta=30^@#