After deploying her parachute, a skydiver falls through the air with a constant speed of 7.00 m/s . As she falls, there is a constant breeze blowing west at 4.50 m/s .
At what standard angle does the parachutist move?
Tan A = Y/X = -7.00/-4.50 = 1.55555.
A = 57.3o W. of S.
To find the standard angle at which the parachutist moves, we need to analyze the horizontal and vertical components of her motion.
First, let's consider the horizontal motion. The constant breeze blowing west at 4.50 m/s is responsible for the horizontal velocity of the parachutist. We can assume that the parachutist is not affected by any horizontal forces other than the wind. Therefore, her horizontal velocity is 4.50 m/s to the west.
Next, let's move on to the vertical motion. Since the parachutist is falling at a constant speed of 7.00 m/s, we can assume that gravity is balanced by the upward force of air resistance provided by the parachute. The vertical motion is unaffected by the wind.
Now, we can calculate the standard angle at which the parachutist moves using the components of motion. The standard angle is the angle between the resultant velocity vector (the combined velocity due to horizontal and vertical motions) and the horizontal direction.
To find the standard angle, we can use basic trigonometric functions. The standard angle can be calculated as:
tan(theta) = Vertical Component / Horizontal Component
Since the parachutist is falling vertically with a constant speed of 7.00 m/s, the vertical component is 7.00 m/s.
Since the horizontal component is 4.50 m/s to the west, the magnitude of the horizontal component is 4.50 m/s.
Plugging these values into the formula, we get:
tan(theta) = 7.00 m/s / 4.50 m/s
Simplifying this equation, we find:
tan(theta) = 1.56
Now, we can find the angle using the inverse tangent function (arctan):
theta = arctan(1.56)
Using a calculator, we find:
theta ≈ 57.7 degrees
Therefore, the standard angle at which the parachutist moves is approximately 57.7 degrees.
To find the standard angle at which the parachutist moves, we can use trigonometry. The standard angle is the angle between the direction of motion of the parachutist and the positive x-axis.
Let's break down the given information:
- The skydiver falls with a constant speed of 7.00 m/s.
- There is a constant breeze blowing west at 4.50 m/s.
To find the angle, we can use the tangent function. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle.
Let's assume that the direction of the skydiver's motion is the adjacent side, and the westward breeze is the opposite side.
tan(angle) = opposite/adjacent
Using the trigonometric identity tan(angle) = opposite/adjacent, we can rearrange the equation to solve for the angle:
angle = arctan(opposite/adjacent)
In this case, the opposite side is the westward breeze speed and the adjacent side is the speed of the skydiver.
angle = arctan(4.50 m/s / 7.00 m/s)
Using a calculator, we can find the value of the angle.
angle ≈ arctan(0.643)
angle ≈ 33.6°
Therefore, the parachutist moves at a standard angle of approximately 33.6°.