Answer
Verified
414k+ views
Hint: The displacement of an object is the distance between the initial and final point of the sailboat. We will calculate the third displacement of the boat using direction vectors such that the net displacement will be 6 kilometers.
Complete step by step answer
Let us start by giving vector notation to the different displacements of the sail boat as given in the question. For the first displacement, the sail boat moves East which corresponds to the positive $ x $ direction which corresponds to the $ \hat i $ direction in the Cartesian system. So the displacement will be
$ {S_1} = 2\hat i $
In the second displacement, the sail boat moves $ 37^\circ $ south of east which means the displacement will be
$ {S_2} = 5(\cos 37^\circ )\hat i - 5(\sin 37^\circ )\hat j $ which can be written as
$ {S_2} = 4\hat i - 3\hat j $
Let the displacement of the third vector be $ {S_3} $ . Since the net displacement of the boat is 6 kilometers due East, we can write the net displacement $ S $ as
$ S = 6\hat i $
Since the individual displacements should add up to the net displacement, we can write
$ S = {S_1} + {S_2} + {S_3} $
Substituting the value of $ {S_1},{S_2}\,{\text{and}}\,S $ as we derived above, we get
$ 6\hat i = \hat i + 4\hat i - 3\hat j + {S_3} $
Solving for $ {S_3} $ , we get
$ {S_3} = 3\hat j $ which is the third displacement.
Note
While calculating the displacement in the second displacement, the y-component will be negative since the boat is moving in the downwards direction i.e. South of East. Since we’ve been given the displacements of all the three different motions of the boat, they correspond to the distance between the final and the initial points of the boat and hence we can directly use the vector addition of displacements to calculate the net displacement.
Complete step by step answer
Let us start by giving vector notation to the different displacements of the sail boat as given in the question. For the first displacement, the sail boat moves East which corresponds to the positive $ x $ direction which corresponds to the $ \hat i $ direction in the Cartesian system. So the displacement will be
$ {S_1} = 2\hat i $
In the second displacement, the sail boat moves $ 37^\circ $ south of east which means the displacement will be
$ {S_2} = 5(\cos 37^\circ )\hat i - 5(\sin 37^\circ )\hat j $ which can be written as
$ {S_2} = 4\hat i - 3\hat j $
Let the displacement of the third vector be $ {S_3} $ . Since the net displacement of the boat is 6 kilometers due East, we can write the net displacement $ S $ as
$ S = 6\hat i $
Since the individual displacements should add up to the net displacement, we can write
$ S = {S_1} + {S_2} + {S_3} $
Substituting the value of $ {S_1},{S_2}\,{\text{and}}\,S $ as we derived above, we get
$ 6\hat i = \hat i + 4\hat i - 3\hat j + {S_3} $
Solving for $ {S_3} $ , we get
$ {S_3} = 3\hat j $ which is the third displacement.
Note
While calculating the displacement in the second displacement, the y-component will be negative since the boat is moving in the downwards direction i.e. South of East. Since we’ve been given the displacements of all the three different motions of the boat, they correspond to the distance between the final and the initial points of the boat and hence we can directly use the vector addition of displacements to calculate the net displacement.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Which are the Top 10 Largest Countries of the World?
One cusec is equal to how many liters class 8 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
The mountain range which stretches from Gujarat in class 10 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths