# Simplifying:t \approx 0.34 secondsCalculating Hang Time for Vertical Jump

• mandaa123
In summary: Simplifying:t = \sqrt{\frac{1.16}{9.81}} = \sqrt{0.118} = 0.344 seconds.In summary, the hang time of an athlete jumping 0.58 meters vertically can be calculated by using the formula t = sqrt(1.16/9.81), which equals 0.344 seconds. This formula is derived from the concept that total hang time is equal to twice the time it takes for the athlete to go up and come down, which are both equal to each other.
mandaa123

## Homework Statement

Calculate the hang time of an athlete who jumps a vertical distance of 0.58 meter.

## Homework Equations

all i know is that d= 0.5m, and possibly initial velocity is 0? I am not sure.

## The Attempt at a Solution

i tried using v = d/t, even though i doubted it would work.

(this homework is due today, i really need help)

Total time (hang time) = time going up + time coming down.

and, time up = time down

so, 2 X time down = hang time.

for time down use the formula (yes V initial = 0, A = -9.81)

X final = X initial + V initial (t) + 1/2A(t^2)

i understand what formula to use now, but I am having trouble with the math because 0.5m=(-9.81Xt^2) / 2 and i do not know how to solve for t in that, since its squared, but over a fraction and multiplying with 9.81

...well that's order of operations. you will have serious trouble passing without knowing them...

.58m = 0 + 0 + .5 (9.81m/s^2)(t^2)

to get t by itself

1) add or subtract from each side (in this case that part is 0)
2) multiply or divide
3) take your square root

t^2 = the sq root of (.58m / ((.5 times 9.81))

thats the time it takes to go down. doubling it will give you your total hang time.

$$0.58 = \frac{1}{2} \times 9.81 \times t^2$$
Divide both sides by 1/2:
$$\frac{0.58}{\frac{1}{2}} = 9.81 \times t^2$$
Divide both sides by 9.81:
$$\frac{0.58}{\frac{1}{2} \times 9.81} = t^2$$
Since dividing by 1/2 is the same as multiplying by 2:
$$\frac{2 \times 0.58}{9.81} = t^2$$
Taking the square root:
$$\sqrt{\frac{2 \times 0.58}{9.81}} = t$$

## 1. How do I calculate hang time?

Hang time can be calculated by dividing the vertical distance traveled by the object by the acceleration due to gravity (9.8 m/s^2). The equation is: time = √(2 * height/9.8).

## 2. What is the formula for calculating hang time?

The formula for calculating hang time is: time = √(2 * height/9.8), where time is the hang time in seconds, height is the vertical distance traveled in meters, and 9.8 is the acceleration due to gravity in meters per second squared.

## 3. Can I calculate hang time without knowing the height or distance?

No, in order to calculate hang time, you need to know the vertical distance traveled by the object. This can be measured or estimated using other variables, such as the angle of launch and initial velocity.

## 4. How does air resistance affect hang time?

Air resistance can affect hang time by slowing down the object's vertical velocity, leading to a shorter hang time. This effect is more significant for objects with larger surface areas and can be minimized by reducing the object's air resistance through streamlined design or using a denser medium, such as water.

## 5. Can I calculate hang time for any object?

Yes, the equation for calculating hang time can be applied to any object that follows a parabolic path, including projectiles, vehicles, and even animals such as jumping kangaroos. However, the accuracy of the calculation may vary depending on the object's shape and air resistance.

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