a truck travelling due north at 20 m/s turns west and travels at the same speed. the change in its velocity be

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A truck travelling due north at 20 ms^

Click here👆to get an answer to your question ✍️ A truck travelling due north at 20 ms^-1 turns west and travels at the same speed. Then the change in velocity is

A truck travelling due north at 20 ms

Question −1

turns west and travels at the same speed. Then the change in velocity is

A40 ms

−1 northwest

B20

2 ​ ms −1 northwest

C20

2 ​ ms −1 southwest

D40 ms

−1 southeast Medium Open in App Solution Verified by Toppr

Correct option is C)

A truck travelling due north at a 20ms

−1

turns west and travel  at the same speed. Then from the Pythagoras theorem, the resultant velocity will be given by hypotenuse ( the starting point and the ending point) as

∣Δv∣= 20 2 +20 2 ​ =20 2 ​

and it will be directed towards southwest

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A truck travelling due to north at 20m s^(

From (figure) vec(v)(1)=20hat(j) and vec(v)(2)=-20hat(i). Deltavec(v)=vec(v)(2)-vec(v)(1)=-20(hat(i)+hat(j)) |Deltavec(v)=20sqrt(2) and dirction theta^(-1)=45^(@),i.e.,S-W

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A truck travelling due to nort...

A truck travelling due to north at

20m s −1 20ms-1

turns west and travels at the same speed. Find the change in its velocity.

Updated On: 27-06-2022

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Text Solution Open Answer in App Solution From (figure) v ⃗ 1 =20 j ˆ v→1=20j^ and v ⃗ 2 =−20 i ˆ v→2=-20i^ . Δ v ⃗ = v ⃗ 2 − v ⃗ 1 =−20( i ˆ + j ˆ )

Δv→=v→2-v→1=-20(i^+j^)

∣ ∣ Δ v ⃗ =20 2 – √ ∣Δv→=202 and dirction θ −1 = 45 ∘ θ-1=45∘ ,i.e.,S-W

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A truck travelling due north at 20 m / s turns west and travels at the same speed. The change in its velocity isA. 40 m / s northwestB. 20 √2 m / s northwestC. 40 m / s southwestD. 20 √2 m / s southwest

A truck travelling due north at 20 m / s turns west and travels at the same speed. The change in its velocity isA. 40 m / s northwestB. 20 √2 m / s northwestC. 40 m / s southwestD. 20 √2 m / s southwest

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A truck travelling due north at 20 m / s turns west and travels at the same speed. The change in its velocity isA. 40 m / s northwestB. 20 √2 m / s northwestC. 40 m / s southwestD. 20 √2 m / s southwest

Question

A truck travelling due north at

20 m/s

turns west and travels at the same speed. The change in its velocity is

A 40 m/s northwest B 20 √ 2 m/s northwest C 40 m/s southwest D 20 √ 2 m/s southwest Solution

Step 1, Given data

The truck is travelling with the speed =

20 m s − 1 due north

The truck turns in west and travel with the speed=

20 m s − 1

Given situation can be drawn as

Step 2: Concept and formula used:

The change in velocity of a body is given by the difference between the final velocity and initial velocity of the body.

The unit vector along the positive direction of the x-axis is given by

^ i

and along the negative x direction is given by

− ^ i

whereas the unit vector along the positive direction of the y-axis is given by

^ j

and along the negative x direction is given by

− ^ j

to represent the direction of a vector along the axis.

If the velocity is given in the vector form that is;

v = v x ^ i + v ^ y j

The magnitude of the resultant is given by;

| → v | = √ ( v x 2 + v 2 y )

Step 3: Calculation of the change in its velocity:

The velocity of the truck in the north direction can be represented in the vector form as;

→ v 1 = 20 ^ j

The velocity of the truck in the west direction can be represented in the vector form as;

→ v 2 = − 20 ^ i Thus, Change in velocity( Δ → v )= → v 2 − → v 1 Δ → v = − 20 ^ i − ( 20 ^ j ) Δ → v = − 20 ^ i − 20 ^ j Δ → v = − 20 ( ^ i + ^ j ) Now,

The magnitude of the change in velocity will be;

∣ ∣ → Δ v ∣ ∣ = √ ( − 20 m s − 1 ) 2 + ( − 20 m s − 1 ) 2 ∣ ∣ → Δ v ∣ ∣ = √ 400 + 400 ∣ ∣ → Δ v ∣ ∣ = √ 800 ∣ ∣ → Δ v ∣ ∣ = 20 √ 2 m s − 1

The truck is moving from south to north and then turns towards the west. Hence the direction is taken as southwest.

Thus,

Option D)

20 √ 2 m s − 1

along southwest direction is the correct option.

PhysicsStandard XII Suggest Corrections 8

SIMILAR QUESTIONS

Q.

A truck travelling due north at 20m/s turns west and travels at same speed. The change in velocity be

PhysicsStandard XII

Q. A truck travelling due to North at 20 m/s turns East and travels at the same speed. The change in its velocity is -

PhysicsStandard XII View More

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