Answer:
v = 376.06 mph
, θ = 41.23º
Explanation:
This exercise can be solved with the addition of vectors, we have two vectors: the speed of the airplane 400 mph in the 45 direction to the north east and the speed of the wind coming from the north, therefore the wind direction is south.
One way to solve these exercises is to use trigonometry to break down the speed of the plane.
v₁ₓ = v₁ cos 45
= v₁ sin45
v₁ₓ = 400 0.707
v₁ₓ = 282.84 mph
v_{1y} = 282.84 mph
Wind speed is
v₂ = 35 mph
Let's add each speed
vₓ = v₁ₓ
vₓ = 282.84 mph
v_{y} = v_{1y} - v₂
v_{y} = 282.84 - 35
v_{y} = 247.84 mph
The result can be done in two ways
v = (282.84 i ^ + 247.84 j ^) mph
And in the form of a module and angle, for which we use the Pythagorean theorem and trigonometry
v = √ (vₓ²+ v_{y}²)
v = √ (282.84² + 247.84²)
v = 376.06 mph
tan θ = v_{y} / vₓ
θ = tan⁻¹ (247.84 / 282.84)
θ = 41.23º
Answer:
Angle of refelction is 60°
Explanation:
Let two mirrors XY and ZY meet at Y such that ∠XYZ = 30°
Let an incident ray PO incident on the 1st mirror XY and is parallel to the 2nd mirror YZ.
Let ON be the normal.
Now we know that , angle of incidence is equal to the angle of reflection
∴∠PON = ∠NOQ =60°
Therefore, the angle of reflection of the ray incident on the 1st mirror is 60 degree.
The bowling ball would have the most inertia because it has the most mass. Inertia is the ability to resist a change in motion. So, it sort of makes sense that the more massive an object, the more resistance it has against outside forces.
Bowling ball would be your answer since it has the most mass.
Explanation:
Using Kinematics,
We have v = u + at.
=> v = (5m/s) + (2.0m/s²)(4.0s)
=> v = 13m/s.
Hence the child's speed is now 13m/s.
Answer:
36° and 144°
Explanation:
Supplementary angles are angles that have their total sum to be 180°.
If the measurement of those angles are in the ratio 1:4, this means angle 180° is divided in the ratio of 1:4.
If the total ratio is 1+4 = 5, the minimum angle will be;
1/5×180° = 36°
The maximum angle will be;
4/5×180° = 144°
Therefore the measures of the angles are 36°and 144°