- #1

phantomvommand

- 265

- 39

- Homework Statement
- A boy enters a patch of ice with a coefficient of friction µ with speed v.

By running on the ice, the boy turns his velocity vector by 90◦ in the minimum possible time, so

that his final speed is also v. What is the minimum possible time, and what kind of curve is the

trajectory? Assume the normal force with the ice is constant.

- Relevant Equations
- v = u + at

My guess was simply that as acceleration changes from the north to east direction, the total magnitude change of v is ##v \sqrt 2##.

Acceleration is ##\mu g##, so time would be ##\frac {v \sqrt 2} {\mu g}##. This agrees with the textbook solution.

What I do not understand is the trajectory taken. Supposedly, because acceleration is constant, the answer is parabola. How is this arrived at? For example, acceleration in circular motion (at constant speed v) is also constant, so I do not see why constant acceleration means that it must be a parabola (and not a circle, or anything else!).

Many thanks for any help.

Acceleration is ##\mu g##, so time would be ##\frac {v \sqrt 2} {\mu g}##. This agrees with the textbook solution.

What I do not understand is the trajectory taken. Supposedly, because acceleration is constant, the answer is parabola. How is this arrived at? For example, acceleration in circular motion (at constant speed v) is also constant, so I do not see why constant acceleration means that it must be a parabola (and not a circle, or anything else!).

Many thanks for any help.