Question

Question 3 A woman sitting in a stationary car notices a man cycling past her at 40 km/hr. Five seconds after he passes her car, she starts following after him. What is the shortest possible distance in which she will catch up to the cyclist if he maintains hrs speep and she obeys the speed limit of 70 km/hr? The car has a maximum acceleration
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Answer 1

The shortest possible distance in which she catches up with the man is 129.7 m.

The given parameters:

speed of the man, v₁ = 40 km/hr

speed of the woman, v₂ = 70 km/hr

time when the woman started moving, t₁ = 5 seconds

To find:

• the shortest distance when she catches up with the man

Convert the given speed in km/h to m/s

• 3.6 km/h = 1 m/s
• 40 km/h = 40/3.6 = 11.11 m/s
• 70 km/h = 70/3.6 = 19.44 m/s

Calculate the distance moved by the man before she started following him.

Distance moved by the man = speed x time

                                                = 11.11 m/s  x  5 s

                                                = 55.55 m

Let the time the woman catches up with the man = t

Apply the following simple principle to calculate the time.

The man is moving forward and the woman is moving forward to close the gap between them, thus both speeds are working against each other.

$(v_2-v_1)t = 55.55 \ m$

• the difference in the speed is because they are working against each other.

$(19.44 - 11.11)t = 55.55\\\\8.33t = 55.55\\\\t = \frac{55.55}{8.33} \\\\t = 6.67 \ s$

The time when the woman catches up with the man = 6.67 s

The shortest distance at which the woman catches up with the man is calculated as;

Shortest distance = woman's speed x time when she catches up

                               = 19.44 m/s    x  6.67 s

                               = 129.7 m

Thus, the shortest possible distance in which she catches up with the man is 129.7 m.

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