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The velocity-time graph for the vertical component of the velocity of a body thrown upwards from the ground and landing on the roof of a building is given in the figure. The height of the building is:(A) 50 m(B) 40 m(C) 20 m(D) 30 m(E) 10 m

Last updated date: 20th Jun 2024
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Hint: We know that the velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion. An object which moves in the negative direction has a negative velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion, as we can see that in this case, a positive acceleration. Velocity is a vector quantity; it has magnitude which is speed and direction. Even though the speed is constant in this particular example, the direction changes all the time. The velocity of an object changes when the net force acting on it is not zero. Based on this concept we have to solve this question.

So, now the height $=\dfrac{1}{2}\times 30\times 3-\dfrac{1}{2}\times 10\times 1$
$=\dfrac{1}{2}\times 90-\dfrac{1}{2}\times 10$
$=45-5=40m$