The diagram shows a boat crossing a river. The motor makes the boat move north relative to the water at 4.0 m/s. The river water flows east at 3.0 m/s. A re...
Question 1 Report
The diagram shows a boat crossing a river. The motor makes the boat move north relative to the water at 4.0 m/s. The river water flows east at 3.0 m/s. A rescue team wants to predict the boat's resultant velocity relative to the river bank. The arrows are drawn at right angles. The boat travels for 50 s before reaching the far side.
(a) Calculate the magnitude of the resultant velocity of the boat. [2]
(b) Which direction does the boat move relative to the bank? [1]
(c) What distance does the boat travel relative to the bank in 50 s, using your answer to part (a)? [1]
The table below shows results from a student who timed a battery-powered cart over different distances on a straight track. The same cart, battery and light gates were used each time. The student wishes to decide whether the cart moved at constant speed. Distances were measured from the start line to the second light gate.
| distance travelled / m | time / s |
|---|---|
| 0.60 | 0.50 |
| 1.20 | 1.00 |
| 1.80 | 1.50 |
| 2.40 | 2.00 |
(a) Calculate the cart's speed using the 2.40 m result. [2]
(b) Which statement describes the results: constant speed or increasing speed? [1]
(c) Sketch the shape of a distance-time graph for these results. [1]
Answer Details
Boat crossing the river
(a) The northward and eastward velocities are perpendicular, so \(v=\sqrt{4.0^2+3.0^2}=\sqrt{25}=5.0\text{ m/s}\). [2]
(b) The boat moves north-east, or east of north, relative to the bank. [1]
(c) \(d=vt=5.0\times50=250\text{ m}\). [1]
Battery cart
(a) \(v=d/t=2.40/2.00=1.2\text{ m/s}\). [2]
(b) The results show constant speed: each distance divided by its corresponding time gives \(1.2\text{ m/s}\). [1]
(c) A constant speed produces a straight distance-time line through the origin with positive gradient.
[1]
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