2025 NASS PRELIMS P1 Q12

2025 NASS PRELIMS P1 Q12

Secondary 4
7 marks
2025 Ngee Ann Secondary School Prelims A Math Paper 1

The diagram shows Car \(B\), 50 km due east of Car \(A\). Both cars start moving at the same time. Car \(A\) travels due north at a constant speed of 120 km/h while Car \(B\) travels due west at a constant speed of 90 km/h.

  1. The distance between Car \(A\) and Car \(B\) at time \(t\) hours after the cars started moving is noted by \(D\) km. Show that \(D=\sqrt{14400t^2+(50-90t)^2}\).[2]
  2. Given that \(t\) can vary, find the stationary value of \(D\).[4]
  3. Show that this stationary value of \(D\) gives the minimum distance between the two cars.[1]

Solution:

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Answer:(a) \(D=\sqrt{14400t^2+(50-90t)^2}\text{ km}\) (b) \(40\text{ km}\) (c) Minimum, since \(\left.\frac{d^2D}{dt^2}\right|_{t=0.2}>0\).

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