Determining the time it takes to reach half of a penny's terminal speed

In summary, the terminal speed of a penny is 11 m/s and the question is to calculate how long it takes for a penny falling from rest to reach half of this speed. The equation needed is Vf-Vi/a = delta T, but it does not need to be so complicated. Instead, consider using a simpler equation and determining which one is needed based on the given data.
  • #1
aquirk
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The question is:
The terminal speed of a penny is 11 m/s. By neglecting air resistance, calculate how long it takes for a penny falling from rest to reach half of this speed


Homework Equations


I thought maybe you had to use one of the kinematic equations but that didnt work


The Attempt at a Solution


I tried Vf-Vi/a = delta T
Also, I tried dividing 11 m/s by gravity and that didnt work.
Im not sure if I am totally missing an equation needed or if I am making this way harder than it really is. Any help would be greatly appreciated!
 
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  • #2
you are on track with the answer, but why use 11ms-1? (as you stated earlier that it was the terminal velocity, and you were going to use half of the terminal velocity.

Also, the equation does not need to be so complicated. Look at these ones, and figure out which one is needed, by knowing the data you have and the what is in the equations.
 
  • #3


I can provide a response to this question. To determine the time it takes for a penny falling from rest to reach half of its terminal speed, we need to use the equation for acceleration due to gravity, which is a = g = 9.8 m/s^2. This equation is applicable as we are neglecting air resistance in this scenario. We also need to use the equation for velocity, which is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

In this case, the initial velocity (u) is 0 m/s, as the penny is falling from rest. The final velocity (v) is half of the terminal speed, which is 11 m/s/2 = 5.5 m/s. The acceleration (a) is the acceleration due to gravity, which is 9.8 m/s^2. We can rearrange the equation to solve for time (t):

t = (v-u)/a

Substituting the values, we get:

t = (5.5 m/s - 0 m/s)/9.8 m/s^2 = 0.56 seconds

Therefore, it takes approximately 0.56 seconds for a penny falling from rest to reach half of its terminal speed of 11 m/s, neglecting air resistance. This calculation assumes that the penny is in a vacuum and there is no air resistance acting on it. In reality, air resistance will affect the speed at which the penny falls, so this calculation may not be entirely accurate. However, it provides an estimate and gives us an idea of the time it takes for a penny to reach half of its terminal speed.
 

FAQ: Determining the time it takes to reach half of a penny's terminal speed

1. How is the terminal speed of a penny determined?

The terminal speed of a penny is determined by its size, shape, and mass. These factors affect the air resistance acting on the penny as it falls, which eventually balances out the force of gravity and results in a constant speed.

2. Why is it important to determine the time it takes to reach half of a penny's terminal speed?

This calculation can provide insight into the physics of free fall and help understand the relationship between air resistance and gravitational force. It can also be used in various applications, such as designing parachutes or determining the optimal speed for skydiving.

3. What is the formula for calculating the time it takes to reach half of a penny's terminal speed?

The formula for calculating the time it takes to reach half of a penny's terminal speed is t = (m/2g) * ln(1 + (2mg/kvt)), where t is time, m is mass, g is gravitational acceleration, k is the air resistance constant, and vt is the terminal speed.

4. How does air resistance affect the time it takes for a penny to reach half of its terminal speed?

The greater the air resistance acting on the penny, the longer it will take for the penny to reach half of its terminal speed. This is because air resistance slows down the penny's acceleration, meaning it takes longer to reach a constant speed.

5. Can the time it takes for a penny to reach half of its terminal speed be accurately measured in real-life situations?

In real-life situations, factors such as air currents and variations in air resistance can affect the accuracy of the measurement. However, with precise conditions and proper equipment, the time can be measured with a reasonable level of accuracy.

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