Given vectors d (3.00 m, 315 degrees wrt x-axis) and e (4.50 m, 53.0 degrees wrt x-axis), find the resultant r= d + e. (a) write r in vector form. (b) write r showing the magnitude and direction in degrees.

Explanation:

Knowing the magnitude and directions relative to the x axis, we can find the Cartesian representation of the vectors using the formula

where its the magnitude and θ.

So, for our vectors, we will have:

and

Now, we can take the sum of the vectors

This is R in Cartesian representation, now, to find the magnitude we can use the Pythagorean theorem

To find the direction, we can use

As we are in the first quadrant, this is relative to the x axis.

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.