point y is in the interior of xwz. given that and are opposite rays and mxwy4(mywz), mywz = 36°
Opposite rays:- Opposite rays are the rays, which shares a common initial point, but points towards opposite directions. Angle between two opposite rays is 180°.
According to the question,
m∠XWY = 4(m∠YWZ) (Given)
As the two rays WX and WZ are opposite rays, the initial points of those are same. Here in the question, it is W.
∴∠XWZ = 180°
∴m∠XWY + m∠YWZ = 180°
⇒ 4(m∠YWZ) + m∠YWZ = 180°
⇒ 5(m∠YWZ) = 180°
⇒ m∠YWZ = 180°/5
⇒ m∠YWZ = 36°
Thus we can conclude that, m∠YWZ = 36°.
To know more about opposite rays refer below link:
brainly.com/question/28216147
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Answer:
Part a)

Part b)

Part c)

Part d)

Part e)

Part f)

Explanation:
As we know that catapult is projected with speed 19.9 m/s
so here we have


similarly we have


Part a)
Horizontal displacement in 1.03 s



Part b)
Vertical direction we have
![y = v_y t - \frac{1]{2}gt^2](https://tex.z-dn.net/?f=y%20%3D%20v_y%20t%20-%20%5Cfrac%7B1%5D%7B2%7Dgt%5E2)


Part c)
Horizontal displacement in 1.71 s



Part d)
Vertical direction we have
![y = v_y t - \frac{1]{2}gt^2](https://tex.z-dn.net/?f=y%20%3D%20v_y%20t%20-%20%5Cfrac%7B1%5D%7B2%7Dgt%5E2)


Part e)
Horizontal displacement in 5.44 s



Part f)
Vertical direction we have
![y = v_y t - \frac{1]{2}gt^2](https://tex.z-dn.net/?f=y%20%3D%20v_y%20t%20-%20%5Cfrac%7B1%5D%7B2%7Dgt%5E2)


The energy that the rope absorbs from the climber is Ep=m*g*h where m is mass of the climber, g=9.81m/s² and h is the height the climber fell. h=4 m+2 m because he was falling for 4 meters and the rope stretched for 2 aditional meters. The potential energy stored in the rope is Er=(1/2)*k*x², where k is the spring constant of the rope and x is the distance the rope stretched and it is
x=2 m. So the equation from the law of conservation of energy is:
Ep=Er
m*g*h=(1/2)*k*x²
k=(2*m*g*h)/x² = (2*60*9.81*6)/2² = 7063.2/4 =1765.8 N/m
So the spring constant of the rope is k=1765.8 N/m.