Respuesta :
Answer:
The angle is 28.64°
Explanation:
Given:
Radius of curve [tex]r = 120[/tex] m
Tangential acceleration [tex]a_{t} = 1[/tex] [tex]\frac{m}{s^{2} }[/tex]
Total acceleration [tex]a = 2[/tex] [tex]\frac{m}{s^{2} }[/tex]
From equation total acceleration,
[tex]a = \sqrt{a_{t}^{2}+ a_{c}^{2} }[/tex]
Find centripetal acceleration,
[tex]a_{c} = \sqrt{a^{2}- a_{t} ^{2} }[/tex]
[tex]a_{c} = \sqrt{4-1 }[/tex]
[tex]a_{c} = 1.73[/tex] [tex]\frac{m}{s^{2} }[/tex]
From equation of centripetal acceleration,
[tex]a_{c} = \frac{v^{2} }{r}[/tex]
[tex]v = \sqrt{a_{c} r }[/tex]
[tex]v = \sqrt{207.6}[/tex]
[tex]v = 14.41[/tex] [tex]\frac{m}{s}[/tex]
From the equation of kinematics,
[tex]d = \frac{v^{2} }{2a_{t} }[/tex]
[tex]d = \frac{207.6}{2 \times 1.73}[/tex]
[tex]d = 60[/tex] m
For finding the angle,
[tex]d = r\theta[/tex]
[tex]\theta = \frac{d}{r}[/tex]
[tex]\theta = \frac{60}{120}[/tex]
[tex]\theta = 0.5[/tex] rad
[tex]\theta =[/tex] 28.64°
Therefore, the angle is 28.64°
