# Homework Help: Using vectors as a function of time

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1. Sep 3, 2015

### PAstudent

1. The problem statement, all variables and given/known data

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.

2. Relevant equations
magnitude= sqrt( quantities squared added together)

3. 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?

2. Sep 3, 2015

### 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.

3. Sep 3, 2015

### PAstudent

Thank you, I will try that soon

4. Sep 3, 2015

### 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

5. Sep 4, 2015

### haruspex

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