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You calculate that to throw an object vertically to a height h it needs to be launched with an initial upward velocity v 0 , assuming no air resistance. The dashed lines in Fig. show the motion according to this calculation. Which of the velocity - time graphs shows the motion of an object tossed with initial upward velocity v’ 0 that will also rise to height h, but this time with air resistance?

You calculate that to throw an object vertically to a height h it needs to be launched with an initial upward velocity v0 , assuming no air resistance. The dashed lines in Fig. show the motion according to this calculation. Which of the velocity - time graphs shows the motion of an object tossed with initial upward velocity v’0 that will also rise to height h, but this time with air resistance?

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
The correct option is: (B).
It is important to note that velocity versus time graph does not depends on height h but on the initial velocity v’0. In presence of air resistance, a force D = bv acts opposite to the direction of motion of object. If mass of the object is m, the acceleration experienced by object due to air resistance is D/m.
Therefore, the net acceleration on the object moving upward is g + \frac{D}{m}
The final velocity v of the object after any time t is:
236-920_200.PNG
Divide the numerator and denominator of the term on the right hand side by t,
236-385_201.PNG
236-1541_202.PNG
Thus, (B) is the correct option and the rest are ruled out.

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