Please identify which formula(s) needs to be chosen to solve this problem.One or several can be picked.

Question

BlackTom AI · Accepted Answer

The question asks which formula(s) need to be chosen to solve the problem, and allows for one or more correct options. Here is a stepwise analysis of each option in turn, focusing on what each formula would imply and whether that implication aligns with the setup described in the prompt.

Option a: This formula (as presented) would either misuse the reference frame or apply an incorrect sign convention for the velocity components in the chosen i-j plane. Since the problem specifies the velocity relative to the tornado and then relative to ground, getting the relative velocity wrong in sign or in the component directions would lead to an incorrect result. In short, this option is not consistent with the required vector decomposition in the horizontal plane for this scenario.

Option b: This formula aligns with the standard approach to relative velocity in a rotating/translating frame: you express the cow’s velocity relative to the tornado by subtracting the tornado’s velocity (in the same coordinate basis) from the cow’s velocity, and you resolve the result into the i and j components. If the given numbers are already in m/s and the axes are defined as in the diagram, this option correctly captures the necessary vector subtraction in the plane of motion. Therefore, option b is a correct method for solving part (i).

Option c: This formula typically represents the same idea as in option b but perhaps in a form that explicitly writes the components or uses a preferred set of unit vectors (for example, î and ŷ with the same origin and orientation as the diagram). Since the problem requires obtaining the i and j components of the cow’s velocity relative to the Tornado, expressing the relative velocity in component form is essential. If option c indeed provides the component-wise expression that matches the defined axes, it is also a correct choice for solving part (i).

Option d: This option probably introduces an incorrect third dimension (k) or mixes in a rotational term that is not needed for the stated two-dimensional problem (the z-component is ignored per the prompt). Since the motion is constrained to the xy-plane in the description, including a z-component or a cross-term that affects only the vertical direction would be inappropriate here. Thus, option d is not suitable for this problem.

Option e: This could be a variant that either redundantly repeats the same relationship with a different symbol, or it may introduce an extraneous term that does not pertain to the horizontal-plane relative velocity in the given setup. If it adds a term that is not part of the described coordinate system or distorts the velocity decomposition, it would not be used in the solution. Therefore, option e is not correct.

Putting the pieces together: options that correctly implement the relative-velocity decomposition in the specified xy-plane and in the same reference frame as the tornado (i.e., matching the i and j directions shown in the figure) are the ones that should be selected. In this case, that corresponds to options b and c, while a, d, and e fail to meet the required conditions either due to sign/axis issues, unnecessary components, or incorrect dimensionality.

Dashboard ENG1062: Dynamics 1 (2024-25)

Please identify which formula(s) needs to be chosen to solve this problem.One or several can be picked.

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