A sky-diver falls vertically from a helicopter and reaches constant (terminal) velocity.

Question 22

A sky-diver falls vertically from a helicopter and reaches constant (terminal) velocity. The graph shows the variation with time t of the speed v of the sky-diver.

Which graph shows the variation with time t of the distance d fallen by the sky-diver?

Reference: Past Exam Paper – June 2018 Paper 12 Q7

Solution:

Answer: C.

The speed of the sky-diver increases at a decreasing rate until it becomes constant (where terminal velocity is reached).

From a distance-time graph, the speed may be obtained by the gradient of the graph.

So, in the distance-time graph, the gradient should increase at a decreasing rate (a curve) and then becomes constant and non-zero (a straight line, but not horizontal). [B and D are incorrect]

From the velocity-time graph of the sky-diver, initially the speed is zero. So, the gradient of the distance-time graph should be zero initially (that is, the graph should be horizontal initally). [C is correct]

Choice A cannot be correct because the non-zero gradient at time t = 0 shows a non-zero velocity. Only graph C has a zero velocity at time t = 0.