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A Ball is thrown verticall upward with a velocity ‘u’ from the balloon descending with a constant velocity ‘v’. The ball will pass by the balloon after time ?


4 years ago

							The question needs the basic understanding of motion to solve it.considering the downward direction to be +ve and taking ground as the reference point, we have : initial velocity of ball thrown upward using relative motion = –[u-v]constant velocity of ballon = v acceleration of thrown ball = gassume the ball meets the balloon after time ‘t’concept : the time when ball meets the balloon, both will have same displacement in the +ve direction according to our assumption of direction.according to second law of kinematics, we have :displacement of ball = displacement of balloon-[u-v]t +1/2gt2 =vt=> t[gt/2 – u] =0=> t = 2u/ghence required time is 2u/g.thanku !

4 years ago
							Dear Ranjeet Kumar,How can you Take Displacement of ball be “vt” .It should be “vt+1/2gt2.Its right Answer is 2(u+v)/g.I know the answer. But dont know how to solve.

4 years ago
							mr. kuldeep pal, it has been given in the question that the ballon is decending with a constant velocity ‘v’, so we can’t take any acceleration or decelaration.

4 years ago
							Dear Kuldeep, the velocity u of the ball must be with respect to the balloon. Then, taking the upward direction as positive we have:Initial velocity of the ball = uConstant velocity of the balloon = -vLet the ball meets the balloon after a time t.Displacement of the balloon after time t = -vt , which is also the displacement of the ball.Now, applying  , we get                          Solving, we get  , which is the required answer.

4 years ago
							Dear raman the gist of question is that if we take intial velocity of ball with respect to ground to be ‘u’, then the answer will be , but if we are taking initial velocity to be ‘u’ with respect to balloon then the answer will be t = 2u/g.

4 years ago
							Ohh...sorry for the typing mistake. It should read: ‘...the velocity u of the ball must be with respect to the ground’. Apologies.

4 years ago
							I’m in a shock that a 12th pass student has asked me this question when a 11th moving student can answer this with 5 min. Sorry for acting oversmart. So here’s the solution- Relative velocity of all with respect to the baloon  = u + vNow 0=-(u+v)+gtwhich gives, t=u+v/gbut this isn’t the time of flight.We know that time of flight, T=2t=2(u+v)/gPerhaps that’s the right answerhere’s another way to solve it:-We equa=> -vt = ut - (1/2)gt2 [Since in the case of balloon the acceleration is zero]=> -v = u - (1/2)gt => (1/2)gt = u + v => t = 2(u+v)/g And please don’t ask me why there’s minus, okay fine I’ll answer- I use down as negative and upward as positive, so following the convention, v will be negative and u will be positive

3 years ago
							I didn’t explain in the previous answer, so here’s the explanation:-A projectile aquires the speed of the body, in the direction it’s going (the projectile’s direction). So the speed of the ball thrown would be u+v. (since it has it’s own speed as well)So, Time of ascent=u+v/g           …....(A)       Time of descent=u+v/g         …...(B)       Time of flight= 2(u+v)/g                   (A+B)No neeed to say thanks

3 years ago
							And equaling the displacement of the ball and balloon would be wrongMeant to say we cannot solve using-vt=ut-1/2gt2Though the answer would be the same but this isn’t the correct way, not at all

3 years ago
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