Using vectors as a function of time

[PAstudent]

Homework Statement

Vector P is a function of time t.

In a specified coordinate system P is given by: P= (A+Bt)i + (A+Ct-Dt^2)j and P is in meters when t is seconds

Given these values (shown without their units): A=15.0, B=7.00, C=20.0, D=4.00

(a) Calculate the time when P points in the +x direction.

(b) Calculate the magnitude of P at the time calculated in part a.

(c) Calculate the time when P make an angle of -45 degrees with the +x axis.

(d) Calculate the magnitude of P at the time calculated in part c.

Homework Equations

magnitude= sqrt( quantities squared added together)

The Attempt at a Solution

I am mostly confused on part a and c. So for a, would you find where t=0 in the j direction which would leave you with only the i direction which is the +x? For part c, would have something to do with dot product because it includes an angle of 45 degrees?
[/B]

 

[andrewkirk]

The convention is that i represents the x direction and j the y direction.
So for P to point in the x direction the coefficient of j in your equation must be zero. So you need to find what value of t makes that coefficient zero.

For c the ratio of coefficient of j to coefficient of i has to be -1 (think of the angle that the line from (0,0) to (1,-1) makes with the x axis), so that gives you another equation to solve.

 

[PAstudent]

Thank you, I will try that soon

 

[PAstudent]

So for a) 15.0+20.0t-4.00t^2=0 then that comes to 5.66 seconds
b) sqrt(15.0+7.00 x 5.66)= 54.6 m

 

[haruspex]

So for a) 15.0+20.0t-4.00t^2=0 then that comes to 5.66 seconds
b) sqrt(15.0+7.00 x 5.66)= 54.6 m

Looks about right, except for the mention of the 'sqrt(' function.