Vector Representation of Quantities (Velocity, etc.): CCSS.Math.Content.HSN-VM.A.3 - Common Core: High School - Number and Quantity
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Bob is cruising south down a river at 
, and the river has 
current due west. What is Bob's actual speed?
Bob is cruising south down a river at
In order to figure this out, we need to create a picture.
Since bob is traveling south, and the current is traveling west, they are perpendicular to each other. This means that they are 
to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed Bob is actually going.
Recall that the Pythagorean Theorem is 
, where 
is the hypotenuse, and 
, 
are the legs of the triangle, and 
have a 
angle between them.
For our calculations, let 
, and 
.
In order to figure this out, we need to create a picture.
Since bob is traveling south, and the current is traveling west, they are perpendicular to each other. This means that they are
Recall that the Pythagorean Theorem is
For our calculations, let
Compare your answer with the correct one above
Amanda is cruising north down a river at 
, and the river has 
current due east. What is Amanda's actual speed?
Amanda is cruising north down a river at
In order to figure this out, we need to create a picture.
Since Amanda is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed Amanda is actually going.
Recall that the Pythagorean Theorem is , where is the hypotenuse, and , are the legs of the triangle, and have a angle between them.
For our calculations, let 
, and 
.
In order to figure this out, we need to create a picture.
Since Amanda is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are
Recall that the Pythagorean Theorem is
For our calculations, let
Compare your answer with the correct one above
Jack slides down a hill at 
, and throws a rock behind him at 
. How fast is the rock going?
Jack slides down a hill at
Since the rock is going in the opposite direction of Jack, we simply subtract the speed of the rock from how fast Jack is going down the hill.
Since the rock is going in the opposite direction of Jack, we simply subtract the speed of the rock from how fast Jack is going down the hill.
Compare your answer with the correct one above
If an airplane is flying south at 
, and there are winds coming from the west at 
, how fast is the plane going?
If an airplane is flying south at
In order to figure this out, we need to create a picture.
Since the airplane is traveling south, and the wind is coming from the west, they are perpendicular to each other. This means that they are to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed the airplane is actually going.
Recall that the Pythagorean Theorem is , where is the hypotenuse, and , are the legs of the triangle, and have a angle between them.
For our calculations, let 
, and 
.
In order to figure this out, we need to create a picture.
Since the airplane is traveling south, and the wind is coming from the west, they are perpendicular to each other. This means that they are
Recall that the Pythagorean Theorem is
For our calculations, let
Compare your answer with the correct one above
Jill slides down a hill at 
, and throws a coin forward at . How fast is the coin going?
Jill slides down a hill at
Since the coin is going in the same direction as Jill, we simply add the speed of the coin and how fast Jill is going down the hill.
Since the coin is going in the same direction as Jill, we simply add the speed of the coin and how fast Jill is going down the hill.
Compare your answer with the correct one above
Bob slides down a hill at 
, and throws his wallet behind him at 
. How fast is his wallet going?
Bob slides down a hill at
Since Bob's wallet is going in the opposite direction, we simply subtract the speed of the wallet from how fast Bob is going down the hill.
Since Bob's wallet is going in the opposite direction, we simply subtract the speed of the wallet from how fast Bob is going down the hill.
Compare your answer with the correct one above
John is cruising north down a river at 
, and the river has 
current due east. What is John's actual speed?
John is cruising north down a river at
In order to figure this out, we need to create a picture.
Since John is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed John is actually going.
Recall that the Pythagorean Theorem is , where is the hypotenuse, and , are the legs of the triangle, and have a angle between them.
For our calculations, let 
, and 
.
In order to figure this out, we need to create a picture.
Since John is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are
Recall that the Pythagorean Theorem is
For our calculations, let
Compare your answer with the correct one above
Jack slides down a hill at 
, and throws a rock ahead of him at 
. How fast is the rock going?
Jack slides down a hill at
Since the rock is going in the same direction as Jack, we simply add the speed of the rock to how fast Jack is going down the hill.
Since the rock is going in the same direction as Jack, we simply add the speed of the rock to how fast Jack is going down the hill.
Compare your answer with the correct one above
If an airplane is flying south at , and there are winds going north at , how fast is the plane going?
If an airplane is flying south at
Since the airplane and the wind are going in opposite directions, we simply subtract the speed of the wind from the speed of the plane.
Since the airplane and the wind are going in opposite directions, we simply subtract the speed of the wind from the speed of the plane.
Compare your answer with the correct one above
If an airplane is flying south at 
, and there are winds going south at 
, how fast is the plane going?
If an airplane is flying south at
Since the airplane and the winds are going the same direction, we simply add the airplane and wind speeds together.
Since the airplane and the winds are going the same direction, we simply add the airplane and wind speeds together.
Compare your answer with the correct one above
An arrow is shot eastward at 
, and there are winds going west at 
, how fast the arrow going?
An arrow is shot eastward at
Since the arrow and the wind are going in opposite directions, we simply subtract the wind speed from the speed of the arrow.
Since the arrow and the wind are going in opposite directions, we simply subtract the wind speed from the speed of the arrow.
Compare your answer with the correct one above
A ship is sailing northeast ward at 
, and there are winds going southwest ward at 
. How fast is the ship going?
A ship is sailing northeast ward at
Since the direction of the ship and the wind are going in opposite directions, we simply subtract the speed of the wind from the speed of the ship.
Since the direction of the ship and the wind are going in opposite directions, we simply subtract the speed of the wind from the speed of the ship.
Compare your answer with the correct one above
Bob is cruising south down a river at , and the river has current due west. What is Bob's actual speed?
Bob is cruising south down a river at
In order to figure this out, we need to create a picture.
Since bob is traveling south, and the current is traveling west, they are perpendicular to each other. This means that they are to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed Bob is actually going.
Recall that the Pythagorean Theorem is , where is the hypotenuse, and , are the legs of the triangle, and have a angle between them.
For our calculations, let , and .
In order to figure this out, we need to create a picture.
Since bob is traveling south, and the current is traveling west, they are perpendicular to each other. This means that they are
Recall that the Pythagorean Theorem is
For our calculations, let
Compare your answer with the correct one above
Amanda is cruising north down a river at , and the river has current due east. What is Amanda's actual speed?
Amanda is cruising north down a river at
In order to figure this out, we need to create a picture.
Since Amanda is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed Amanda is actually going.
Recall that the Pythagorean Theorem is , where is the hypotenuse, and , are the legs of the triangle, and have a angle between them.
For our calculations, let , and .
In order to figure this out, we need to create a picture.
Since Amanda is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are
Recall that the Pythagorean Theorem is
For our calculations, let
Compare your answer with the correct one above
Jack slides down a hill at , and throws a rock behind him at . How fast is the rock going?
Jack slides down a hill at
Since the rock is going in the opposite direction of Jack, we simply subtract the speed of the rock from how fast Jack is going down the hill.
Since the rock is going in the opposite direction of Jack, we simply subtract the speed of the rock from how fast Jack is going down the hill.
Compare your answer with the correct one above
If an airplane is flying south at , and there are winds coming from the west at , how fast is the plane going?
If an airplane is flying south at
In order to figure this out, we need to create a picture.
Since the airplane is traveling south, and the wind is coming from the west, they are perpendicular to each other. This means that they are to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed the airplane is actually going.
Recall that the Pythagorean Theorem is , where is the hypotenuse, and , are the legs of the triangle, and have a angle between them.
For our calculations, let , and .
In order to figure this out, we need to create a picture.
Since the airplane is traveling south, and the wind is coming from the west, they are perpendicular to each other. This means that they are
Recall that the Pythagorean Theorem is
For our calculations, let
Compare your answer with the correct one above
Jill slides down a hill at , and throws a coin forward at . How fast is the coin going?
Jill slides down a hill at
Since the coin is going in the same direction as Jill, we simply add the speed of the coin and how fast Jill is going down the hill.
Since the coin is going in the same direction as Jill, we simply add the speed of the coin and how fast Jill is going down the hill.
Compare your answer with the correct one above
Bob slides down a hill at , and throws his wallet behind him at . How fast is his wallet going?
Bob slides down a hill at
Since Bob's wallet is going in the opposite direction, we simply subtract the speed of the wallet from how fast Bob is going down the hill.
Since Bob's wallet is going in the opposite direction, we simply subtract the speed of the wallet from how fast Bob is going down the hill.
Compare your answer with the correct one above
John is cruising north down a river at , and the river has current due east. What is John's actual speed?
John is cruising north down a river at
In order to figure this out, we need to create a picture.
Since John is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed John is actually going.
Recall that the Pythagorean Theorem is , where is the hypotenuse, and , are the legs of the triangle, and have a angle between them.
For our calculations, let , and .
In order to figure this out, we need to create a picture.
Since John is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are
Recall that the Pythagorean Theorem is
For our calculations, let
Compare your answer with the correct one above
Jack slides down a hill at , and throws a rock ahead of him at . How fast is the rock going?
Jack slides down a hill at
Since the rock is going in the same direction as Jack, we simply add the speed of the rock to how fast Jack is going down the hill.
Since the rock is going in the same direction as Jack, we simply add the speed of the rock to how fast Jack is going down the hill.
Compare your answer with the correct one above