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Question 1188713: A body slide down an incline plane which make angle of 30° with the horizontal neglecting friction. Calculate
i) The velocity of the body after sliding 10m from rest.
ii) The time taken to slide 10m distance.
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821)   (Show Source):
Answer by ikleyn(52790)  (Show Source):
You can put this solution on YOUR website! .
A body  SLIDES down  AT incline plane which  MAKES angle of 30° with the horizontal.
Neglecting friction, calculate
a) The velocity of the body after sliding 10m from rest.
b) The time taken to slide 10m distance.
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Pay your attention on how I edited your post, making punctuation correct, in order for the post would have sense.
(a) Notice that the height "h" is half of the hypotenuse, since the angle with horizont is 30.
So, the height is  = 5 meters.
The change of the potential energy between the levels h = 5 meters and h = 0 if P = mgh,
where m is the mass of the body in kilograms and h = 10m/s^2 is the gravity acceleration.
This change of the potential energy is spent to increase the kinematic energy of the body
from 0 to  . where v is the magnitude of the velocity at the end.
So, = mgh. It is nothing elese as the energy conservation law in this problem.
Canceling "m" in both sides, you get  = 2gh, or v =  .
The last step is to substitute h = 5 m, g = 10 m/s^2 into this formula, and you get
v =  =  = 10 m/s.
ANSWER. The final speed (the magnitude of the velocity) is 10 m/s.
(b) In this problem, the speed rise from 0 to 10 m/s uniformly with time.
Hence, the average speed is the average between 0 and 10 m/s, which is 5 m/s.
It implies that the time taken to slide is the full distance of 10 meters divided by the average speed of 5 m/s
time taken to slide =  = 2 seconds.
Solved. // Both questions are answered.
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