  We construct the D3-brane dual to a $k$-quark of $\mathcal{N}=4$
super-Yang-Mills theory in the totally symmetric representation of $SU(N)$,
undergoing arbitrary motion. Our method of construction generalizes previous
work by Mikhailov, and proceeds by shooting light rays inward from the anti-de
Sitter boundary, to trace out the brane embedding. We expect this method to
have wider relevance, and provide evidence for this by showing that it
correctly reproduces the known D5-brane embeddings dual to totally
antisymmetric $k$-quarks. As an application of our solutions, we compute the
energy of the D3-brane and extract from it the $k$-quark's intrinsic energy and
rate of radiation. The result matches expectations based on previous
calculations, and makes contact with the exact Bremsstrahlung function for the
fundamental representation.
