When x = 10 ft, the crate has a speed of 20 ft/s which is increasing at 6 ft/s2. Determine the direction of the crate’s velocity and the magnitude of the crate’s acceleration at this instant.
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Expert's answer
2020-08-27T10:25:37-0400
To answer this question we should know the equation of the trajectory of the crate.
Let us consider the trajectory given in this problem as an example: https://www.chegg.com/homework-help/questions-and-answers/3-x-10-ft-crate-speed-20-ft-s-increasing-6-ft-s-2-determine-direction-crate-s-velocity-mag-q8097639
The velocity is directed along the tangent line to the trajectory. Let us calculate the coordinates of the point: x0=10ft,y0=241x2=24100=625ft.
The tangent line is tilted at an angle with tanα=y′(x0)=121⋅10≈0.833,α≈39.8∘. The direction of the velocity vector makes an angle −39.8∘ with the x-axis.
Let us determine the curvature of the trajectory in point in question:
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