A woman is riding a Jet Ski at a speed of 28 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 = 28 m/s
r = ?
g = 9.81 m/s^2
Theta = 20 degrees
r = (28 m/s)^2 /(tan(20) x (9.81 m/s^2))
r is estimated to be about 219.574 m
Am I correct in this case?
Well, I must say your calculations are quite impressive! However, I must remind you that I am a Clown Bot, not a math genius. So, I can't really verify your answer. But hey, who needs accurate calculations when we can just rely on clown physics, right? So, I would say the minimum distance from the seawall that she can start her turn and avoid a crash is approximately one million banana peels or five cartwheels in length. It should do the trick! Now go out there and make those Jet Ski calculations fly! Or, well, swim, I guess.
Yes, you are correct in calculating the radius of the turn. The formula you used, r = (v^2) / (g * tan(theta)), is the correct formula for calculating the radius of a turn on a banked curve. Plugging in the values v = 28 m/s, g = 9.81 m/s^2, and theta = 20 degrees, you get an estimated radius of about 219.574 m.
Yes, your calculations are correct. To find the minimum distance from the seawall, you need to determine the radius of the turn. In this case, you can use the equation for the radius of a banked curve:
r = (v^2) / (g * tan(θ))
Where:
- r is the radius of the turn,
- v is the speed of the Jet Ski,
- g is the acceleration due to gravity, and
- θ is the angle of the banked curve or the lean angle in this case.
By substituting the given values:
- v = 28 m/s
- g = 9.81 m/s^2 (acceleration due to gravity)
- θ = 20 degrees
Plugging these values into the formula, you correctly calculated the radius of the turn to be approximately 219.574 m. This means that in order to avoid a crash, the woman should start making her turn at a distance of at least 219.574 meters away from the seawall.