Question

A truck travelling due east at 50 m/s turns north and travels at the same speed. The change in its velocity will be

(1) 50 m/s NW
(2) 50✓2 m/s NW
(3) 50 m/s NE
(4) 50✓2 m/s NE

please explain​

Answer 1

Answer:

Option (4).

Explanation:

Truck travels at a speed of 50 m / s in East.

Velocity of truck this time : 50 m / s E = A { let }

Then after, truck turns north and travels with the same speed 50 m / s.

Velocity of truck = 50 m / s N = B ( let )

Using vectors addition laws :

= > Resultant velocity = √( A² + B² ) { Since both are at 90°, ABcos90° = 0 } { A & B are now representing the magnitude of vectors }

= > Change in velocity = √( 50² + 50² ) m / s

= > Change in velocity = 50√( 1 + 1 ) m / s

= > Change in velocity = 50√2 m / s

Now, as shown in the attachment, direction of the resultant velocity is NE.

Therefore,

= > The change in velocity will be 50√2 m / s NE.

Answer 2

Answer:

$\sf 50\sqrt{2} \ m/sec \ NE$

4. option is correct.

Explanation:

Given :

A truck is travelling due to east at 50 m / sec = $\sf -50 \ \hat{i}$

It turns north with same speed = $\sf 50 \ \hat{j}$

We are asked to find change is velocity i.e. Δ v

$\sf \longrightarrow 50 \ \hat{j} - (-50) \ \hat{i}$

$\sf \longrightarrow 50 \ \hat{j} +50 \ \hat{i}$

$\sf \longrightarrow 50 \ \hat{i} +50 \ \hat{j}$

Now resultant velocity :

$\sf \longrightarrow \sqrt{(50)^2 +(50)^2}$

$\sf \longrightarrow \sqrt{2(50)^2}$

$\sf \longrightarrow 50\sqrt{2} \ m/sec \ NE$

Therefore , change in its velocity will be 50 √ 2 m / sec NE .