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A body projected vertically up crosses points A & B separated by 28 m with velocities one third and one fourth of initial velocity respectively. What is the maximum height reached by it above the ground.  
Please answer it fast sir
Thank You

Hello Ankit,

Use the kinematic formula
Vf^2 = Vi^2 + 2*a*y
We know that Vfa = Vi/3 and Vfb = Vi/4.

At point A:
Vfa^2 = Vi^2 + 2*(-9.8 m/s^2)*Ya
Solving for Vi^2
Vi^2 = Vfa^2 + 2*(9.8 m/s^2)*Ya
Substituting for Vfa
Vi^2 = (Vi/3)^2 + 2*(9.8 m/s^2)*Ya
Vi^2 = (1/9)*Vi^2 + 19.6 m/s^2*Ya
(8/9)*Vi^2 = 19.6 m/s^2*Ya
Vi^2 = (9/8)*19.6 m/s^2*Ya = 22.05 m/s^2*Ya

At point B:
Vfb^2 = Vi^2 + 2*(-9.8 m/s^2)*(Ya+28 m)
Solving for Vi^2
Vi^2 = Vfb^2 + 2*(9.8 m/s^2)*(Ya+28 m)
Substituting for Vfb
Vi^2 = (Vi/4)^2 + 2*(9.8 m/s^2)*(Ya+28 m)
Vi^2 = (1/16)*Vi^2 + 2*(9.8 m/s^2)*(Ya+28 m)
(15/16)*Vi^2 = 2*(9.8 m/s^2)*(Ya+28 m)

I'm going to leave some work for you to do in return for quickly answering. You have one more step to do to the above expression to give you an expression for Vi^2 equivalent to the bottom line of the point A analysis. Then you will have 2 expressions for Vi^2. Set those equal to each other and work out what Ya is. Knowing Ya, you can then plug it into the bottom line of the point A analysis to find Vi. Knowing Vi, you can plug it into the basic kinematic formula (the top equation above), with Vf=0, to find max height.

I hope this helps,


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Steve Johnson


I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.


I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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