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A glider is initially moving at a constant height of 3.72 m. It is suddenly subject to a wind such that its velocity at a later time t can be described by the equation v(t) = 16.02i − 7.96(1 + t)j + 0.76t3k, where v and its components are in meters per second, t is in seconds, and the z axis is perpendicular to the level ground. (a) What was the initial velocity of the glider? (Express your answer in vector form.)

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Answer:

[tex]17.89\ \text{m/s}[/tex]

Explanation:

Velocity is given by

[tex]v(t) = 16.02\hat{i}-7.96(1 + t)\hat{j} + 0.76t^3\hat{k}[/tex]

Initial velocity is asked so t = 0

[tex]v(0)=16.02\hat{i}-7.96(1+t)\hat{j}+0.76\times 0\hat{k}\\\Rightarrow v(0)=16.02\hat{i}-7.96\hat{j}[/tex]

Magnitude is given by

[tex]|v|=\sqrt{16.02^2+(-7.96)^2}\\\Rightarrow |v|=17.89\ \text{m/s}[/tex]

The initial velocity of the glider was [tex]17.89\ \text{m/s}[/tex].

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