A skydiver is jumping from an airplane traveling at 10.0 m/s. The plane is 3520 m above the earth. The sky diver pulls his cord at 1760 m above the earth. Neglecting air resistance, how far does the skydiver travel horizontally before pulling the cord?

Δh=H-h= gt²/2

t=sqrt(2•Δh/g)=
=sqrt{2• (3520-1760)/9.8}=18.95 s.
s=vt=10•18.95=189.5 m

To determine the horizontal distance traveled by the skydiver before pulling the cord, we need to analyze the horizontal motion of the skydiver.

Since there is no air resistance, the only force acting on the skydiver in the horizontal direction is their initial horizontal velocity. This means that the horizontal velocity of the skydiver remains constant throughout the fall.

Given that the plane is traveling at 10.0 m/s horizontally, we can assume that the skydiver also has the same horizontal velocity of 10.0 m/s.

Next, we need to find the time it takes for the skydiver to fall from 3520 m to 1760 m. We can use the equation of motion:

delta_y = v_iy * t + (1/2) * a_y * t^2

where:
- delta_y is the change in vertical position (1760 m - 3520 m = -1760 m)
- v_iy is the initial vertical velocity (which is 0 m/s because the skydiver is momentarily at rest before jumping)
- a_y is the acceleration due to gravity (-9.8 m/s^2)

By substituting the known values into the equation, we can solve for the time, t:

-1760 m = 0 m/s * t + (1/2) * (-9.8 m/s^2) * t^2
-1760 m = -4.9 m/s^2 * t^2

Simplifying the equation, we get:

t^2 = 360

Taking the square root of both sides, we find:

t ≈ 18.97 seconds

Now that we know the time it takes for the skydiver to fall from 3520 m to 1760 m, we can calculate the horizontal distance traveled:

d = v_ix * t

where:
- d is the horizontal distance
- v_ix is the initial horizontal velocity (10.0 m/s)
- t is the time (18.97 seconds)

d = 10.0 m/s * 18.97 s
d ≈ 189.7 meters

Therefore, the skydiver travels approximately 189.7 meters horizontally before pulling the cord.

To calculate the horizontal distance traveled by the skydiver before pulling the cord, we need to find the time it takes for the skydiver to reach the pull cord height and then use that time to find the horizontal distance traveled.

Step 1: Find the time taken to reach the pull cord height:
The skydiver is initially at a height of 3520 m and pulls the cord at a height of 1760 m. The difference in height is 3520 m - 1760 m = 1760 m.

Using the equation of motion:

d = v0 * t + (1/2) * a * t^2

where d is the displacement, v0 is initial velocity, t is time and a is acceleration.

Since the skydiver is moving vertically downward, its initial velocity (v0) is -10.0 m/s (taken as negative).

At the highest point (when the skydiver pulls the cord), the velocity of the skydiver will be 0 m/s. The acceleration (a) is -9.8 m/s^2.

Using the equation above for the vertical displacement d = -1760 m, and solving for t, we have:

-1760 m = -10.0 m/s * t + (1/2) * (-9.8 m/s^2) * t^2

Rearranging the equation and solving for t, we get a quadratic equation:

-4.9 t^2 - 10.0 t - 1760 = 0

Using quadratic formula t = (-b ± √(b^2 - 4ac))/(2a), where a = -4.9, b = -10.0, and c = -1760, we can find the time t.

t = (-(-10.0) ± √((-10.0)^2 - 4 * -4.9 * -1760))/(2 * -4.9)

Calculating this equation gives us two possible values for t: t1 = 4.0 s and t2 ≈ -71.4 s.
Since time cannot be negative, we discard the negative value, and we have t = 4.0 s.

Step 2: Calculate the horizontal distance traveled:
To find the horizontal distance traveled by the skydiver, we need to use the horizontal component of the velocity.

The vertical component of velocity does not affect the horizontal motion of the skydiver since there is no acceleration in the horizontal direction.

Therefore, the horizontal distance traveled can be calculated as:

d_horizontal = v_horizontal * t

where v_horizontal is the horizontal component of velocity and t is the time taken to reach the pull cord height.

Since the skydiver is initially traveling with a velocity of 10.0 m/s horizontally, the horizontal component of velocity is the same.

Hence, d_horizontal = 10.0 m/s * 4.0 s = 40.0 m

Therefore, the skydiver travels 40.0 meters horizontally before pulling the cord.