A skydiver deploys his parachute when he is 910 directly above his desired landing spot. He then falls through the air at a steady 5.4 . There is a breeze blowing to the west at 1.0 .

Question

A skydiver deploys his parachute when he is 910 directly above his desired landing spot. He then falls through the air at a steady 5.4 . There is a breeze blowing to the west at 1.0 .

Part A
At what angle with respect to vertical does he fall?

By what distance will he miss his desired landing spot

Answer 1

Please show some Units.

Answer 2

To find the angle at which the skydiver falls with respect to the vertical, we can use trigonometry.

Let's consider a right triangle with the vertical distance the skydiver falls as the opposite side (910 ft) and the horizontal distance he travels as the adjacent side (unknown). The hypotenuse of the triangle is the distance the skydiver moves through the air (which we know is 5.4 ft/s).

Using the trigonometric ratio for the tangent function, we can write:

tan(theta) = opposite/adjacent

tan(theta) = 910 ft/adjacent

To find the adjacent side (horizontal distance), we can rearrange the formula:

adjacent = opposite / tan(theta)

Now, let's calculate the angle.

theta = atan(opposite/adjacent)

theta = atan(910 ft / (5.4 ft/s))

Using a calculator, we find:

theta ≈ 89.192 degrees

So, the skydiver falls at an angle of approximately 89.192 degrees with respect to the vertical.

Now let's move on to Part B to find the distance by which he will miss his desired landing spot.