A submarine starts at the surface, where the depth is 0 metres. Depths below the surface are recorded as negative numbers. It dives 480 m, then rises 150 m....
Question 1 Report
A submarine starts at the surface, where the depth is 0 metres. Depths below the surface are recorded as negative numbers.
- It dives 480 m, then rises 150 m. Work out its depth after these changes. (2)
- From this depth, it then dives at 60 m per minute for 4 minutes. Work out its new depth. (3)
- The crew must bring it to exactly \(-400\) m using 5 equal rises. Work out the size, in metres, of each rise. (3)
- Was the total distance dived greater than the total distance risen for the whole exercise? Show your working. (2)
Answer Details
This question tests applying directed-number changes to depth, multiplying a rate by a time, solving for an equal-sized repeated change, and comparing two accumulated totals.
- (a) [2] Diving is a decrease in depth and rising is an increase: \[-480 + 150 = -330\text{ m}\]
- (b) [3] Diving at \(60\) m per minute for \(4\) minutes is a further decrease of \(60 \times 4 = 240\) m: \[-330 - 240 = -570\text{ m}\]
- (c) [3] The total rise needed to go from \(-570\) m to \(-400\) m is \[-400 - (-570) = 170\text{ m}\] Divided equally across \(5\) rises, each rise is \[170 \div 5 = 34\text{ m}\]
- (d) [2] Total distance dived \(= 480 + 240 = 720\) m. Total distance risen \(= 150 + 170 = 320\) m. Since \(320 < 720\), the total distance dived was indeed greater than the total distance risen.
Distances dived or risen are always positive quantities even though the depth itself is recorded as negative; keep the running depth (signed) and the total distance travelled (always positive, found by adding magnitudes) as two separate calculations.
Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning