# Help with Vector Excel lab

I have to do this problem using Microsoft Excel.

A motorboat leaves the dock and travels in a direction 15 degrees East of North for 20 minutes at a constant speed of 20 miles/hour. At that point the boat abruptly changes its direction to 20 degrees South of West and its speed to 25 miles/hour and continues on that new course for 35 minutes. Assuming that the lake is still, calculate the answers to the following questions:
(a) What is the boat's displacement (magnitude and direction) after 55 minutes?
(b) What is the total distance travelled by the boat?
(c) What is the boat's average velocity (magnitude and direction) after 55 minutes?
(d) What is the boat's average speed after 55 minutes?

First leg: (15 degrees East of North)
Time ? minutes
Speed ? miles/hr
Magnitude of displacement #1 ? miles

Second leg: (20 degrees South of West)
Time ? minutes
Speed ? miles/hr
Magnitude of displacement #2 ? miles

Choose the +x coordinate as East and the +y coordinate as North.
Find the x and y components of the two displacement vectors.
x-comp. y-comp.
displacement #1 ? ?
displacement #2 ? ?
total displacement ? ?
magnitude direction
total displacement ? ?
total distance travelled ?
average velocity ? ?
average speed ?

Obviously each area with a ? needs data or an equation filled in there. If some people can guide me through this, it'd be greatly appreciated.

## Answers and Replies

I guess what I don't understand in the first part is, they want the magnitude of displacement 1. That'd just be d=tv, but t is in minutes, and v is in miles/hr, and you're supposed to keep the answer in miles/hr. When I enter the formula into the "Magnitude of displacement #1 ? miles" part, should I just enter =(11/12)*B16? 11/12 would be the 55 minutes as a fraction of 1 hour, and the B16 is just the cell where the 20 miles/hr is.

*Edit: neglect this. I was using the 11/12 incorrectly, I meant 1/3 in the first part*

Last edited:
Here's what I got so far

First leg: (15 degrees East of North)
Time 20 minutes
Speed 20 miles/hr
Magnitude of displacement #1 6.6666667 miles

Second leg: (20 degrees South of West)
Time 35 minutes
Speed 25 miles/hr
Magnitude of displacement #2 14.58333333 miles

Choose the +x coordinate as East and the +y coordinate as North.
Find the x and y components of the two displacement vectors.

x-comp, y-comp
displacement #1: 6.44, 1.73
displacement #2: 13.70, 4.99
total displacement: 20.14, 6.71
magnitude
total displacement: 21.23

"total displacement: 21.23"

Then to get the direction, I took the inverse tangent of (6.71/20.14) and got 18.4 degrees.

Can anyone verify what I have so far?

Now how should I go about the total distance, average velocity, and average speed?

bump, come on