Answer:
(a) 2.85 m
(b) 16.5 m
(c) 21.7 m
(d) 22.7 m
Explanation:
Given:
v₀ₓ = 19 cos 71° m/s
v₀ᵧ = 19 sin 71° m/s
aₓ = 0 m/s²
aᵧ = -9.8 m/s²
(a) Find Δy when t = 3.5 s.
Δy = v₀ᵧ t + ½ aᵧ t²
Δy = (19 sin 71° m/s) (3.5 s) + ½ (-9.8 m/s²) (3.5 s)²
Δy = 2.85 m
(b) Find Δy when vᵧ = 0 m/s.
vᵧ² = v₀ᵧ² + 2 aᵧ Δy
(0 m/s)² = (19 sin 71° m/s)² + 2 (-9.8 m/s²) Δy
Δy = 16.5 m
(c) Find Δx when t = 3.5 s.
Δx = v₀ₓ t + ½ aₓ t²
Δx = (19 cos 71° m/s) (3.5 s) + ½ (0 m/s²) (3.5 s)²
Δx = 21.7 m
(d) Find Δx when Δy = 0 m.
First, find t when Δy = 0 m.
Δy = v₀ᵧ t + ½ aᵧ t²
(0 m) = (19 sin 71° m/s) t + ½ (-9.8 m/s²) t²
0 = t (18.0 − 4.9 t)
t = 3.67
Next, find Δx when t = 3.67 s.
Δx = v₀ₓ t + ½ aₓ t²
Δx = (19 cos 71° m/s) (3.67 s) + ½ (0 m/s²) (3.67 s)²
Δx = 22.7 m
This question is incomplete because the options are missing; here is the complete question:
A runner starts at point A, runs around a 1-mile track, and finishes the run back at point A. Which of the following statements is true?
A. The runner's displacement is 1 mile.
B. The runner's displacement is zero.
C. The distance the runner covered is zero.
D. The runner's speed was zero.
The answer to this question is B. The runner's displacement is zero
Explanation:
Displacement always implies a change of position; this means an object or individual moves from point A to point B, and therefore the original position is different from the final position. Additionally, in displacement, other related factors such as the total distance the body moved and the direction of movement. In the case presented, it can be concluded there was no displacement or the displacement is zero because even when the runner moved and ran two miles, he returned to the initial position, and without a change in the position, there is no displacement.
A force is a push or pull upon an object resulting from the object's interaction with another object.
Answer: 1.88 N
Explanation:
Data:
Force = 4.00N
angle = 62°
horizontal force = ?
Solution:
The trigonometric ratio that relates horizontal - leg to hypotenuse is the cosine.
That ratio is:
horizontal - leg
cos(angle) = -------------------------
hypotenuse
So, applied to the force, that is:
horizontal force
cos (angle) = -----------------------------------
total force
So, clearing the horizontal component you get:
horizontal force = force * cos (angle)
Substitute the data given:
horizontal force = 4.00N * cos(62°) = 4.00N * 0.4695 = 1.88 N
Answer: 1.88N
Temperature increase, smaller container, or influx of more gas
