If you are initially 1.50 km [E] of home and 0.65 hours later you are 0.75 km [N 45 degrees E] of home, what is your change in displacement?

To find the change in displacement, we need to calculate the difference between your initial and final positions.

Your initial position is given as 1.50 km [E] of home. This means you are 1.50 km east of your home.

Your final position is given as 0.75 km [N 45 degrees E] of home. This means you are 0.75 km north and 45 degrees east of your home.

To calculate the change in displacement, we can form a right triangle with the east and north distances as the two sides. The hypotenuse of this triangle will represent the change in displacement.

Using basic trigonometry, we can calculate the change in displacement:

East distance = 1.50 km
North distance = 0.75 km

To find the hypotenuse (change in displacement), we can use the Pythagorean theorem:

(change in displacement)^2 = (East distance)^2 + (North distance)^2

(change in displacement)^2 = (1.50 km)^2 + (0.75 km)^2
(change in displacement)^2 = 2.25 km^2 + 0.5625 km^2
(change in displacement)^2 = 2.8125 km^2

Taking the square root of both sides, we find:

change in displacement = √(2.8125 km^2)
change in displacement ≈ 1.677 km

Therefore, your change in displacement is approximately 1.677 km.