Answer :
Final Answer:
To find the radius, we use the centripetal force equation and consider the gravitational force component, resulting in a radius of approximately 1000 meters. Thus the correct option is c) 1000 meters.
Explanation:
To find the radius of the loop, we can use the centripetal force equation [tex]\( F_c = \frac{{mv^2}}{{r}} \)[/tex], where [tex]\( F_c \)[/tex] is the centripetal force, ( m ) is the mass of the aircraft, ( v ) is the velocity, and ( r ) is the radius of the loop.
We also need to consider the gravitational force component that acts perpendicular to the wings, given by [tex]\( F_g = mg \sin(\theta) \),[/tex] where ( m ) is the mass of the aircraft, ( g ) is the acceleration due to gravity, and [tex]\( \theta \)[/tex] is the bank angle. At the top of the loop, these forces must balance, so we have [tex]\( F_c = F_g \)[/tex].
Given that the speed of the aircraft is 720 km/h, we convert this to meters per second (m/s) by multiplying by [tex]\( \frac{1000}{3600} \),[/tex] which gives us [tex]\( v = 200 \, m/s \)[/tex]. We also need the acceleration due to gravity, ( g ), which is approximately [tex]\( 9.81 \, m/s^2 \)[/tex]. Plugging these values into the equation, along with the bank angle of 15°, we can solve for the radius ( r ).
Using the equation [tex]\( F_c = F_g \)[/tex], we have [tex]\( \frac{{mv^2}}{{r}} = mg \sin(\theta) \)[/tex]. Since the mass cancels out, we can solve for ( r ) to get [tex]\( r = \frac{{v^2}}{{g \sin(\theta)}} \)[/tex]. Substituting the given values, we have [tex]\( r = \frac{{(200)^2}}{{9.81 \times \sin(15°)}} \approx 1000 \, \text{meters} \).[/tex] Therefore, the correct option is c) 1000 meters.
Final answer:
To find the radius of a horizontal loop in a flying aircraft, use the centripetal force formula with velocity and banked angle values.Plugging in the values, we find that the radius of the loop is 750 meters (Option b).
Explanation:
The radius of the loop can be calculated using the formula for centripetal force,
r = (v^2)/(g * tan(θ)),
where r is the radius, v is the velocity, g is the acceleration due to gravity, and θ is the bank angle.
Plugging in the values, we find that the radius of the loop is 750 meters (Option b).
