Finding the Magnitude of a Displacement Vector with Multiple Components

[thschica]

During a rodeo, a clown runs 8.0 m north, turns 35 degrees east of north, and runs 3.5 m. Then, after waiting for the bull to come near, the clown turns due east and runs 5.0 m to exit the arena. What is the magnitude of the clown's total displacement?


When I did this I got a trapazoid shape and I tried to solve it but I got 10.3 and 16.6.How am I supposed to do one like this?

 

[ComputerGeek]

total displacement is the distance from the start point to the finish point. find that distance and you solve the problem. you should not be getting a trapezoid unless he started where he finished. if that is the case, you do not need any math.

 

[Townsend]

During a rodeo, a clown runs 8.0 m north, turns 35 degrees east of north, and runs 3.5 m. Then, after waiting for the bull to come near, the clown turns due east and runs 5.0 m to exit the arena. What is the magnitude of the clown's total displacement?


When I did this I got a trapazoid shape and I tried to solve it but I got 10.3 and 16.6.How am I supposed to do one like this?

You have three vectors, right? Do you know how to add vectors by adding their components? Just do this to get the final position of the clown. Then you just need to find the magnitude of that vector.

To get you started your second vector is
$$3.5*<cos(55), sin(55)>$$

Now just figure out what the other two vectors are and just add 'em up. Then use you're good friend, the pythagorean theorem to find the magnitude of this vector. Do you understand?