A speedboat heads west at 108 km / h for 20.0 min. It then travels at 60.0^∘ south of west at 90

step 1 Okay, so this question is about average velocity. And so we have the speedboat, and it has two s

A speedboat heads west at 108 km / h for 20.0 min. It then...

Key Concepts

Average Speed

Average speed is defined as the total distance traveled divided by the total time taken. It is a scalar quantity and does not take into account the direction of travel.

Average Velocity

Average velocity is the net displacement divided by the total time taken. Being a vector quantity, it encompasses both magnitude and direction, making it different from average speed.

Displacement

Displacement refers to the vector representing the shortest distance from the initial to the final position. Unlike distance, it is sensitive to the direction of motion.

Vector Resolution

Vector resolution involves decomposing a vector into its horizontal and vertical components using trigonometric functions such as sine and cosine. This technique is critical when dealing with directions not aligned with the standard coordinate axes.

Trigonometric Analysis in Vectors

Trigonometric analysis in vectors uses the sine and cosine functions to calculate the magnitude of a vector's components, which is necessary for accurate vector addition and determining the overall displacement when the motion involves angled directions.

Transcript

00:01 Okay, so this question is about average velocity.

00:04 And so we have the speedboat, and it has two sort of legs.

00:08 It's traveling at two different speeds, at two different directions.

00:11 And so first we have to calculate the average speed.

00:14 So for the first part of the trip, the boat is heading west in a straight horizontal line for 20 minutes, and it's traveling at 108 kilometers per hour.

00:26 And then the second part of the trip, it starts traveling at 60 degrees south.

00:31 Of west and so it'll look something like this right or if we have this vertical line this is south and this vertical line will be west so this is this is 60 degrees and we know that it's traveling 90 kilometers per hour and it's going to be and it's going to be happening for 10 minutes okay so what is the average speed well the average speed is pretty easy we just do it as sort of weighted out calculation where we have 108 kilometers per hour so our average speed is with a hundred eight kilometers per hour times 20 minutes okay plus the 90 kilometers per hour happening at ten for ten minutes so we just divide this whole thing with a total time which is 30 minutes and we get our answer of the average speed being 102 kilometers per hour so that's the answer for a part b you have to find the average velocity now this is very very similar to the average speed part except we got to split this into the x and y components first okay so if we take the second part and we split this into the x and y components kind of like this uh we can do some we can do some math so we just call this 30 degrees you do the other way around doesn't really matter um if we find that the y component of this boat velocity is going to be 77 .9 kilometers per hour and the x component is going to be 45 kilometers per hour right so this is just done using you know right angle sign and coast functions uh you know for example if define 77 .9 all you got to do is you got to multiply 90 cost 30 right now you go 77 .9 okay so that's cool um so let's find the average velocity using the same method that we differ speed for the x component and we'll do it for for the y component and then we'll combine them to.

02:42 Right.

02:43 So we have average x velocity.

02:48 It's going to be equal to.

02:49 It's still just 108 times 20 minutes.

02:53 This time instead of 90 kilometers per hour, it's going to be 45 kilometers an hour for the other 10 minutes.

02:59 And so, dividing this by 30, the average x velocity is going to be 87 kilometers per hour.

03:08 Okay...