Final answer:
The radius of the bobsled turn banked at 75.0° and taken at 30.0 m/s, assuming it is ideally banked, is approximately 42.4 m.
Step-by-step explanation:
To find the radius of a bobsled turn banked at 75.0° and taken at 30.0 m/s, we can use the formula for centripetal force:
F = m * v^2 / r
where F is the centripetal force, m is the mass of the bobsled, v is the velocity, and r is the radius of the turn.
Since the bobsled is ideally banked, we can also use the formula:
r = v^2 / (g * tan(θ))
where g is the acceleration due to gravity and θ is the angle of banking.
Plugging in the values, we get:
r = (30.0 m/s)^2 / (9.8 m/s^2 * tan(75.0°))
Simplifying the equation, the radius of the bobsled turn is approximately 42.4 m.