Calculating the Distance for Different Times

Oct 13, 2025 by miodeya.com 26 views

In the Formula $d=4.9 t^2$ , $d$ is the Total Distance in Meters, and $t$ is the Time in Seconds that the Skydiver Free Falls

Understanding the Formula

The formula $d=4.9 t^2$ is used to calculate the total distance in meters that a skydiver free falls, given the time in seconds. In this formula, $d$ represents the total distance in meters, and $t$ represents the time in seconds. The coefficient $4.9$ is a constant that takes into account the acceleration due to gravity, which is approximately $9.8 \, \text{m/s}^2$ . This formula is derived from the equation of motion under constant acceleration, which is $s = ut + \frac{1}{2}at^2$ , where $s$ is the displacement, $u$ is the initial velocity, $t$ is the time, and $a$ is the acceleration.

Calculating the Distance for Different Times

To calculate the distance the skydiver falls for different times, we can simply plug in the values of $t$ into the formula $d=4.9 t^2$ . Let's consider the following times:

a) $t = 2$ seconds

To calculate the distance the skydiver falls for $t = 2$ seconds, we can plug in the value of $t$ into the formula:

$d = 4.9 t^2$ $d = 4.9 (2)^2$ $d = 4.9 (4)$ $d = 19.6$ meters

Therefore, the skydiver falls a distance of $19.6$ meters in $2$ seconds.

b) $t = 4$ seconds

To calculate the distance the skydiver falls for $t = 4$ seconds, we can plug in the value of $t$ into the formula:

$d = 4.9 t^2$ $d = 4.9 (4)^2$ $d = 4.9 (16)$ $d = 78.4$ meters

Therefore, the skydiver falls a distance of $78.4$ meters in $4$ seconds.

c) $t = 6$ seconds

To calculate the distance the skydiver falls for $t = 6$ seconds, we can plug in the value of $t$ into the formula:

$d = 4.9 t^2$ $d = 4.9 (6)^2$ $d = 4.9 (36)$ $d = 176.4$ meters

Therefore, the skydiver falls a distance of $176.4$ meters in $6$ seconds.

d) $t = 8$ seconds

To calculate the distance the skydiver falls for $t = 8$ seconds, we can plug in the value of $t$ into the formula:

$d = 4.9 t^2$ $d = 4.9 (8)^2$ $d = 4.9 (64)$ $d = 313.6$ meters

Therefore, the skydiver falls a distance of $313.6$ meters in $8$ seconds.

e) $t = 10$ seconds

To calculate the distance the skydiver falls for $t = 10$ seconds, we can plug in the value of $t$ into the formula:

$d = 4.9 t^2$ $d = 4.9 (10)^2$ $d = 4.9 (100)$ $d = 490$ meters

Therefore, the skydiver falls a distance of $490$ meters in $10$ seconds.

Conclusion

In this article, we have used the formula $d=4.9 t^2$ to calculate the distance a skydiver falls for different times. We have shown that the distance the skydiver falls increases quadratically with time, and that the formula can be used to calculate the distance for any given time. This formula is a useful tool for skydivers and physicists alike, and can be used to calculate the distance a skydiver falls in a variety of situations.

References

[1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
[2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.

Discussion

The formula $d=4.9 t^2$ is a simple and powerful tool for calculating the distance a skydiver falls. However, it is worth noting that this formula assumes a constant acceleration due to gravity, which is not exactly true in reality. In reality, the acceleration due to gravity is slightly less than $9.8 \, \text{m/s}^2$ due to the rotation of the Earth and other factors. Therefore, the actual distance a skydiver falls may be slightly less than the calculated value.

It is also worth noting that this formula is only applicable for free fall, and does not take into account other factors such as air resistance. In reality, air resistance can have a significant effect on the distance a skydiver falls, and can cause the skydiver to experience a significant amount of drag.

Overall, the formula $d=4.9 t^2$ is a useful tool for calculating the distance a skydiver falls, but it should be used with caution and in conjunction with other factors such as air resistance.
Q&A: Understanding the Formula $d=4.9 t^2$

Q: What is the formula $d=4.9 t^2$ used for?

A: The formula $d=4.9 t^2$ is used to calculate the total distance in meters that a skydiver free falls, given the time in seconds.

Q: What is the significance of the coefficient 4.9 in the formula?

A: The coefficient 4.9 in the formula takes into account the acceleration due to gravity, which is approximately $9.8 \, \text{m/s}^2$ . This coefficient is derived from the equation of motion under constant acceleration.

Q: How does the formula $d=4.9 t^2$ relate to the equation of motion under constant acceleration?

A: The formula $d=4.9 t^2$ is derived from the equation of motion under constant acceleration, which is $s = ut + \frac{1}{2}at^2$ , where $s$ is the displacement, $u$ is the initial velocity, $t$ is the time, and $a$ is the acceleration.

Q: What are the limitations of the formula $d=4.9 t^2$ ?

A: The formula $d=4.9 t^2$ assumes a constant acceleration due to gravity, which is not exactly true in reality. In reality, the acceleration due to gravity is slightly less than $9.8 \, \text{m/s}^2$ due to the rotation of the Earth and other factors. Additionally, the formula does not take into account other factors such as air resistance.

Q: How does air resistance affect the distance a skydiver falls?

A: Air resistance can have a significant effect on the distance a skydiver falls, and can cause the skydiver to experience a significant amount of drag. This can result in a shorter distance fallen than calculated using the formula $d=4.9 t^2$ .

Q: Can the formula $d=4.9 t^2$ be used to calculate the distance a skydiver falls in a variety of situations?

A: Yes, the formula $d=4.9 t^2$ can be used to calculate the distance a skydiver falls in a variety of situations, such as free fall, skydiving, and parachuting. However, it is essential to consider other factors such as air resistance and the rotation of the Earth.

Q: What are some real-world applications of the formula $d=4.9 t^2$ ?

A: The formula $d=4.9 t^2$ has several real-world applications, including:

Calculating the distance a skydiver falls in a free fall situation
Determining the distance a parachutist falls before opening their parachute
Estimating the distance a person falls from a height in a free fall situation

Q: How can the formula $d=4.9 t^2$ be used in education?

A: The formula $d=4.9 t^2$ can be used in education to teach students about the concept of free fall, the equation of motion under constant acceleration, and the significance of air resistance. It can also be used to demonstrate the relationship between time and distance in a free fall situation.

Q: What are some common misconceptions about the formula $d=4.9 t^2$ ?

A: Some common misconceptions about the formula $d=4.9 t^2$ include:

Assuming that the formula is only applicable for skydiving
Ignoring the effect of air resistance on the distance a skydiver falls
Using the formula to calculate the distance a person falls from a height without considering other factors such as air resistance and the rotation of the Earth.

Q: How can the formula $d=4.9 t^2$ be used in research and development?

A: The formula $d=4.9 t^2$ can be used in research and development to study the physics of free fall, the effect of air resistance on the distance a skydiver falls, and the significance of the coefficient 4.9 in the formula. It can also be used to develop new technologies and equipment for skydiving and parachuting.