Statement I: If a satellite's altitude function has a positive derivative ( ), the satellite is…
Statement I: If a satellite's altitude function $h(t)$ has a positive derivative ($h'(t) > 0$), the satellite is moving away from the Earth.
Statement II: At the apogee (highest point), the instantaneous velocity ($\frac{dh}{dt}$) of the satellite relative to its altitude is zero.
Which of the following is correct?
- aStatement I is true and Statement II is false.
- bStatement I is false and Statement II is true.
- cBoth the statements are true.
- dBoth the statements are false.
Answer
Answer
AIWritten by AI - it can contain mistakes.
Correct option: c
(c) Both the statements are true.
Statement I: If $h'(t) > 0$, the altitude increases with time, so the satellite is moving away from Earth. Thus, Statement I is true.
Statement II: At the apogee (highest point), the altitude attains a maximum, so the instantaneous rate of change of altitude $\frac{dh}{dt} = 0$. Thus, Statement II is true.
From ISC 2027 Specimen Mathematics Paper 1, question 1(v).