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A body is thrown vertically upwards with a velocity of 19.6 m/s. What is the total time for which the body remains in the air (g=9.8 m/s^2)?

We can use equations of motion to solve this equation. The initial and final velocity are related as:


v = u + at


where u is the initial velocity, v is the final velocity, a is the acceleration and t is the time taken.


In this case, when the ball is thrown upwards, u = 19.6 m/s and


a = -g = -9.8 m/s^2. Since the ball's upward motion is resisted by gravity, it will come to a stop. That is, v = 0 m/s.


Hence, 0 = 19.6 + (-9.8)t


solving the equation, we get: t = 2 sec.


Thus, the body will rise up for 2 seconds before coming to rest. It will then start falling down again and take 2 seconds for the downward journey. 


The total time spent in the air = time for upward journey + time for downward journey = 2 s + 2 s =  4 s.


One can also use the other equations of motion:


s = ut + 1/2 at^2 and v^2 = u^2 + 2as


to solve for the distance traveled and time taken for the downward journey to verify that the same time is taken to rise up and come down.


Hope this helps.

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