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?