Simple vector calculus homework problem

icystrike · Mar 30, 2011

Homework Statement

Printed homework problem: a motorcycle on a hill with position r(t) = ti + 0.5t^2 j, reaching the top at t = 1, with parts (a) and (b) on velocity, acceleration, and tangential and normal components; a diagram shows the curve with t = 0 at point A and t = 1 at the top.

Homework Equations

The Attempt at a Solution

Handwritten vector calculus work: position r(t) = <t, t^2/2, 0>, velocity v(t) = <1, t, 0>, acceleration a(t) = <0, 1, 0>, then |v(t)| = sqrt(1+t^2), v(t).a(t) = t, |v(t) x a(t)| = 1, a_T = t/sqrt(1+t^2), a_N = 1/sqrt(1+t^2), and values at t=1 for a_T, a_N, T(t) and T, and N = <-1, sqrt(2)-1, 0>.

LCKurtz · Mar 30, 2011

My only comment would be that the problem is very poorly stated. It is one thing to say the path is given parametrically by r(t) = <t, (1/2)t²> and another thing to say that r(t) describes the position of the motorcycle at time t, t in seconds, which it does not state. The problem is not solvable without assuming that.

icystrike · Mar 30, 2011

oh... i think its their negligence.. But if they have stated that.. will my working be correct? :) Thanks again!

LCKurtz · Mar 30, 2011

icystrike said:

oh... i think its their negligence.. But if they have stated that.. will my working be correct? :) Thanks again!

I think mostly correct. I'm disagreeing with your N by a factor of 1/sqrt(2), but I might be off so check it.

Simple vector calculus homework problem

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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