The given vector represents a hot air balloon that experiences a 0.25m/s^2 up and 0.25 m/s^2 to the right at 45 degrees. find the magnitude of the resultant

when two vectors are inclined at some angle to each other then the magnitude of resultant of two vectors is given as

here A and B are the magnitude of two vectors and theta is the angle between them

now here we know that two vectors are of magnitude 0.25 m/s^2 each and they are inclined at angle of 45 degree

now we will plug in all data above

A = B = 0.25

So the magnitude of resultant acceleration will be 0.46 m/s^2

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diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.