Why Do Different Kinematic Formulas Yield Varied Results for MJ's Jump?

[Dooh]

In this problem, it states that Michael Jordan is able to jump and remain in the air for two full seconds from launch to landing. Use that information to calculate the maximun height that such jump would attain. It also says that MJ's jaximum jump height has been estimated at about one meter.

So, the components that were given are:

t = 2.0s
g = 10 m/s² (rounded from 9.8 for simplicity sake)
and we have to calculate y (height)

Since it takes 2 seconds to go up and down, we can assume that the time it takes for MJ to get to the peak of the jump will be 1.0s, therefore we will use:

t = 1.0s instead.

When i tried solving for this problem, i used the formula:

V_f = V_0 + gt --> V_f - gt = V_0 ,

to solve for initial velocity at takeoff, and i got [ V_0 = 2.2 m/s ]

With that, I followed up with the formula:

a) y = (V_0)(t) + ½gt²

and got the answer of: y = -3.8m , which is obviously wrong. So i tried:

b) y = ½(V_0 + V_f)t

and got the answer: y = 1.1m

My questions are:

1) Why do both formulas give different answers when you are using the same set of data to solve for a problem?

2) Why is formula b correct instead of a when gravity plays a role in this yet it was not part of the formula b?

 

[Doc Al]

When i tried solving for this problem, i used the formula:

V_f = V_0 + gt --> V_f - gt = V_0 ,

to solve for initial velocity at takeoff, and i got [ V_0 = 2.2 m/s ]

Your answer is incorrect. V_0 = gt.

1) Why do both formulas give different answers when you are using the same set of data to solve for a problem?

If you used the correct value for V_0, both formulas would give the same answer. Note that formula (b) relies on V_f being zero, but formula (a) does not.

2) Why is formula b correct instead of a when gravity plays a role in this yet it was not part of the formula b?

Both formulas correctly describe uniformly accelerated motion, but they need the proper data as input.

Question: Are the values given for time and height consistent with each other, given what you know about the laws of physics?

 

[quicknote]

3) How do we know which formula to use in different situations?

I would like to address your questions and provide a response to help clarify the kinematic problem involving MJ.

1) The reason why both formulas give different answers is because they are calculating different things. Formula a is used to calculate the displacement (y) of an object at a specific time (t), while formula b is used to calculate the average displacement of an object over a period of time (t). In this problem, we are looking for the maximum height (y) that MJ's jump would attain, so formula b is more appropriate to use.

2) Formula b is correct because it takes into account the average velocity of the object, which includes the initial and final velocities. In this case, the initial velocity (V_0) is the velocity at takeoff, and the final velocity (V_f) is the velocity at the peak of the jump. Since the object is moving against gravity, the initial velocity is positive and the final velocity is negative. This is why the formula is written as y = ½(V_0 + V_f)t, to account for the direction of the velocities.

3) The choice of formula depends on what information is given and what information is being asked for in the problem. In this case, we were given the time (t) and the estimated maximum jump height (y) and were asked to calculate the initial velocity (V_0). Formula b was appropriate to use because it involves the variables that were given and the one that we were asked to solve for. In other situations, we may be given different variables and may need to use a different formula to solve for the desired quantity.

I hope this helps to clarify the kinematic problem involving MJ. It is important to carefully consider the given information and the desired outcome when choosing the appropriate formula to use in any scientific problem.