A woman is riding a Jet Ski at a speed of 20 m/s and notices a seawall straight ahead. The farthest she can lean the craft in order to make a turn is 20°. This situation is like that of a car on a curve that is banked at an angle of 20°. If she tries to make the turn without slowing down, what is the minimum distance from the seawall that she can begin making her turn and still avoid a crash?
What I did:
v= 20 m/s
g= 9.81 m/s^2
r=?
Theta= 20 degrees
r= (20 m/s)^2 / tan(20) x (9.81 m/s^2)
r is estimated to be 112.027 m
Am I correct in this case?
Yes, your calculation is correct. To find the minimum distance from the seawall that the woman can begin making her turn and still avoid a crash, you need to calculate the radius of the turn. In this case, you can use the equation:
radius = v^2 / (g * tan(theta))
where v is the speed of the Jet Ski (20 m/s), g is the acceleration due to gravity (9.81 m/s^2), and theta is the angle at which the Jet Ski can lean (20 degrees).
Plugging in the values, we get:
radius = (20 m/s)^2 / (9.81 m/s^2 * tan(20 degrees))
Evaluating this expression gives a radius of approximately 112.027 meters.
Therefore, the woman should start making her turn at a distance of at least 112.027 meters from the seawall in order to avoid a crash.