Answer:
The angle at which a turn should be banked depends on the speed of the vehicle, the radius of the turn, and the acceleration due to gravity. To calculate the angle, we can use the following formula:
tanθ = v^2 / (g * r)
where
θ is the angle at which the turn should be banked (in radians)
v is the speed of the vehicle (in m/s)
g is the acceleration due to gravity (approximately 9.81 m/s^2)
r is the radius of the turn (in meters)
Plugging in the values given in the problem, we get:
tanθ = (25 m/s)^2 / (9.81 m/s^2 * 100 m)
tanθ = 6.44
Taking the inverse tangent of both sides, we get:
θ = tan^-1(6.44)
θ ≈ 80.5 degrees
Therefore, the turn should be banked at an angle of approximately 80.5 degrees.