Comparing descent speeds

Warning! Do not attempt to replicate the conditions described in this example!

Comparing descent speeds: parachuting vs. jumping from a window

The descent speed using a D-5 airborne parachute is approximately 5 meters per second in calm weather.

Let us assume the distance from the ground to the bottom of a first-floor window is 2.5 meters.

Compare the descent speeds at ground level for a parachute descent and a jump from a window, neglecting air resistance.

Solution. To compare these two speeds, it is necessary to calculate the speed a person would attain at ground level when jumping from a window.

The speed (Vy) at ground level can be calculated using the formula:

V_{y} = g \cdot t

where g is the acceleration due to gravity (9.8 m/s²), meaning the falling speed increases by 9.8 m/s² every second;

and t is the duration of the descent, measured in seconds (s).

Multiplying the units of free-fall acceleration by the duration of the fall yields units of velocity:

\frac{м}{с^{2}} \cdot с = \frac{м}{с}

The descent height (y) is calculated as follows:

y = \frac{g t^{2}}{2}

From this formula, the descent time (t) can be determined:

t = \frac{2 \cdot h}{g}

Substituting the calculated time into the velocity formula gives the magnitude of the velocity at the moment of impact:

V = \sqrt{2 \cdot g \cdot h}

Substituting numerical values into this formula:

V = \sqrt{2 \cdot 9.8 \cdot 2.5} = 7

Comparing the landing speed with a parachute to the landing speed from a first-floor window.

5 < 7

The descent speed with a D-5 airborne parachute near the ground is lower than the descent speed from a first-floor window.

The calculator shows the body's speed near the Earth's surface. Air resistance is neglected. The formula for determining falling speed is used.

Enter the fall height value h =

V_y=0 (m/s)