While in mid-air

PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

While in mid-air, a

75\,\text{g}

arrow is flying with velocity components

v_x = +35\,\text{m}\,\text{s}^{-1}

and

v_y = +35\,\text{m}\,\text{s}^{-1}

(resulting from an initial

45^{\circ}

launch). A sudden cross-wind delivers a brief lateral impulse

\vec{J}

during a

0.050\,\text{s}

time interval, after which the arrow’s velocity components are

v_x = +35\,\text{m}\,\text{s}^{-1}

and

v_y = +20\,\text{m}\,\text{s}^{-1}

. Air resistance other than the brief gust is negligible, and the arrow’s mass remains constant. (a) Determine the arrow’s change in momentum during the gust. (b) Calculate the magnitude of the impulse delivered by the wind and state its direction relative to the positive

y

–axis. (c) Compute the magnitude of the average force exerted by the wind on the arrow. (d) Discuss whether the wind’s impulse affected the arrow’s kinetic energy, supporting your answer with calculations or reasoning.

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