You're sailboarding at 6.5 m / s when a wind gust hits, lasting 6.3 s accelerating your board at

step 1 So we have an object moving with the velocity equals to 6 .5 meter per second, with acceleration

You're sailboarding at 6.5 m / s when a wind gust hits,...

You're sailboarding at $6.5 \mathrm{m} / \mathrm{s}$ when a wind gust hits, lasting $6.3 \mathrm{s}$ accelerating your board at $0.48 \mathrm{m} / \mathrm{s}^{2}$ at $35^{\circ}$ to your original direction. Find the magnitude and direction of your displacement during the gust.

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Key Concepts

Kinematic Equations

Kinematics provides the tools to relate displacement, velocity, acceleration, and time. In problems with uniform acceleration, the equation s = ut + ½at² is used to calculate the displacement over a time interval given an initial velocity and a constant acceleration, making it fundamental in determining how far an object moves during the period of acceleration.

Vector Decomposition

When acceleration or displacement occurs at an angle, it is often necessary to break the vector into its components along mutually perpendicular axes (usually horizontal and vertical) using trigonometric functions. This decomposition simplifies the problem by allowing each directional component to be analysed separately before the results are combined.

Trigonometric Analysis in Vectors

Trigonometry is used in vector problems to relate the angles and magnitudes of vectors to their horizontal and vertical components. Functions such as sine and cosine enable one to determine the contribution of an angled acceleration to the displacement in each coordinate direction, and to reconstruct the overall vector’s magnitude and direction.

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