Final answer:
The resultant displacement of the toy parachute dropped from a window 13.0m above the ground and travelling 9.0m horizontally is D) 15.8m at a 35-degree angle downward, found using the Pythagorean theorem and trigonometry.
Step-by-step explanation:
To calculate the resultant displacement of the toy parachute, we need to use the Pythagorean theorem because the parachute's motion creates a right triangle with its vertical and horizontal displacements. The vertical displacement is 13.0m from the window to the ground, and the horizontal displacement is 9.0m.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):
c² = a² + b²
Using 13.0m for the vertical side (a) and 9.0m for the horizontal side (b), we get:
c² = 13.0m² + 9.0m²
= 169.0m² + 81.0m²
= 250.0m²
Now take the square root of both sides:
c = √250.0m²
= 15.8m (approximately)
Next, we calculate the angle of the displacement using trigonometry. The angle θ made with the ground can be found using the tangent function:
tan(θ) = opposite/adjacent
= 13.0m / 9.0m
Therefore, θ = arctan(13.0m / 9.0m) which is approximately 55 degrees (55°). However, since the direction is downwards, we subtract this angle from 90° to find the angle with respect to the horizontal plane in a downward direction:
90° - 55° = 35°Hence, the angle is around 35 degrees downward. So the correct answer is 15.8m at a 35-degree angle downward.