Two rockets, and , move along the same straight line far from any planets so that…

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

Two rockets,

R_1

and

R_2

, move along the same straight line far from any planets so that external forces are negligible. Positive velocities are directed to the right. A space probe

P

travels along the same line at an unknown constant velocity

v_P

relative to Earth-based Mission Control (MC). Measured velocities: • Mission Control records

v_{R1}^{\,(\mathrm{MC})}=+7.0\,\text{km}\!\cdot\!\text{s}^{-1}

and

v_{R2}^{\,(\mathrm{MC})}=+3.5\,\text{km}\!\cdot\!\text{s}^{-1}

. • The probe records

v_{R1}^{\,(P)}=+2.0\,\text{km}\!\cdot\!\text{s}^{-1}

and

v_{R2}^{\,(P)}=-1.5\,\text{km}\!\cdot\!\text{s}^{-1}

. (a) Use the data for rocket

R_1

to calculate the probe’s velocity

v_P

relative to Mission Control. State magnitude and direction. (b) Repeat the calculation for

v_P

using the data for rocket

R_2

. Show all algebraic steps. (c) Compare your two results. Are they consistent to within

\pm0.1\,\text{km}\!\cdot\!\text{s}^{-1}

? Justify quantitatively. (d) If the results are not consistent, propose two plausible physical or experimental factors that could explain the discrepancy.

Related theory

Browse the problem library