A mass of 2kg, initially at rest, slides down a frictionless inclined plane of length 1.5 meters in 2.75 seconds. What was the angle of inclination of the plane?

Question

anonymous · Answer

It can be anything since you said it is frictionless

anonymous · Answer

Well, I'm not good at explanation :( 
I hope you get it.

anonymous · Answer

we dont know the angle of inclination, but we do know the distance and time taken to cover that distance which we can use to find the average speed:

velocity = 1.5/2.75 = 0.5454 m/s

find the acceleration

vf=vi+at, since initial velocity was zero, vi = 0, thereforce:
vf=at or a = vf/t = 0.5454/2.75 = 0.1983 m/s^2

$$mgsin\theta=a$$
you already have acceleration
$$sin\theta=a/mg$$
$$\theta=sin^{-1}(a/mg)$$
$$\theta= 1.59^{o}$$

does it look logical ??, how can 2 kg mass slide at that speed/acceleration on 1.59 degree of inclination ?? (maybe correct becoz we assumed its friction less, maybe my calculations are wrong)

anonymous · Answer

oops, i used 0.5454 as acceleration in my calculation, using 0.1983 m/s^2 i get even smaller angle 0.579 degree

anonymous · Answer

16.5 degree