A woman is riding a Jet Ski at a speed of 26 m/s and notices a seawall straight ahead. The farthest she can lean the craft in order to make a turn is 220. This situation is like that of a car on a curve that is banked at an angle of 220. 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?

The minimum distance from the seawall that women can begin making turn is 170.73 m and still avoid crash

Explanation:

According to Newton second law of motion when mass is constant, the product of mass and acceleration is equal to Force.

F = ma

The force that acts on the body moving in the circular path and is directed towards the center around which body is moving is called as centripetal force.

When the body is moving in the circular path with radius r and constant velocity v then object is said to be uniform circular motion.

The object has radial acceleration which is directed radially towards center of the circular path is given by a = v²/r.

F = mv²/r

When the jet ski is moving without skidding in the unbanked curve the static friction between Tyre and the road provide necessary centripetal force.

But when the jet ski is moving in the curve which is banked at angle relative to the horizontal the centripetal force is given by

F = Fₙ sinΘ = mv²/r eqn 1

The vertical component of the normal force is Fₙ cos θ and the jet ski dont accelerate vertically. and hence it must be equal to the weight of the car mg ie

Fₙ cos θ = mg eqn 2

The component of the centripetal force parallel to the banked water which is acting upward must be equal and opposite to the component of the gravity which is acting downward.

Dividing the eqn 1 by 2

tan θ = v²/gr

Rearranging above equation r = v²/g tanθ

r = (26) ²/9.8 tan 22

r = 170.73 m

The minimum distance from the seawall that women can begin making turn is 170.73 m and still avoid crash.