How can I accurately calculate the duration of a free fall jump?

AI Thread Summary
To calculate the duration of a free fall jump from a height of 2.7 meters, the correct approach involves using the equation Y = Yo + VoT + (1/2)gT², where Y represents the height. The initial assumption of using a total distance of 5.4 meters was incorrect, as the man only reaches a height of 2.7 meters before falling back. The initial velocity is assumed to be zero, and the time can be determined by calculating the time for the ascent and then doubling it for the total duration. The correct total time in the air is approximately 1.5 seconds, aligning with the book's answer. Understanding the symmetry of the motion simplifies the calculations.
ScienceGeek
Messages
5
Reaction score
0
A. Here is the stated inquiry:

A man jumps to a vertical height of 2.7 m. How long was he in the air
before returning to Earth?

B. Equations used:

Y = Yo + VoT + (1/2)gT2 (Y because motion is in the vertical direction)

C. Attempted solution:
Because the total distance was twice the man’s highest point (5.4m total) I
used 5.4 rather than 2.7.

Y = Yo + VoT + (1/2)gT2
5.4 = 0 + 0 + ½ (9.8)(t2)
T = 1.05 s

I checked the answer in the back of the book, which was 1.5, but I have been able to come to this solution. Any direction as to what I am doing incorrectly?
 
Physics news on Phys.org
ScienceGeek said:
B. Equations used:

Y = Yo + VoT + (1/2)gT2 (Y because motion is in the vertical direction)
Realize that Y is the object's position (or height), not distance traveled.

C. Attempted solution:
Because the total distance was twice the man’s highest point (5.4m total) I
used 5.4 rather than 2.7.
That's your error. The man never reached a height of y = 5.4m!
 
I attempted calculations using the total displacement as 0, and again as position = 2.7m, but I'm missing something because I just can't get the answer. This seems like it should be much simpler. I'm assuming the initial velocity is zero, but is that an incorrect assumption? Should I be trying to calculate V first?
 
ScienceGeek said:
I'm assuming the initial velocity is zero, but is that an incorrect assumption?
If the initial speed was zero (at the moment he left the ground) how far would he get?

Express the initial velocity in terms of other variables: acceleration and time. (Use another kinematic formula relating them.)

You can also use symmetry to make life easier: The motion going up is the exact reverse of the motion going down. So you only need to find the time it takes for half the motion and then double it.
 
Thank you. I was half-way there, just forgot to double the time.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top