Fiona drops a stone from rest vertically down a water well. She hears the splash of the stone striking the water 1.6 s after the stone leaves her hand. Estimate the

(i) distance between Fiona’s hand and the water surface.

(ii) speed with which the stone hits the water.

After the stone in (a) hits the water surface it rapidly reaches a terminal speed as it falls through the water. The stone leaves Fiona’s hand at time t = 0. It hits the water surface at t₁ and it comes to rest at the bottom of the water at t₂. Using the axes below, sketch a graph to show how the speed v of the stone varies from time t = 0 to just before t = t₂. (There is no need to add any values to the axes.)

Draw and label a free-body diagram representing the forces acting on the stone as it falls through the water at its terminal speed.

(i) s=12.5/12.6 (m);
Allow g =10ms^-2 , answer is 12.8.

(ii) \(v = \sqrt {2gs} \) or gt; (allow any use of suvat equations)
\( = \left( {\sqrt {2 \times 9.8 \times 12.5}  = } \right)15.7\left( {{\rm{m}}{{\rm{s}}^{ - 1}}} \right)\);
Award [2] for a bald correct answer.
Allow g = 10ms^-2 answer is 16.0 ms^-1.
Allow ECF from (a)(i)

straight line to water surface; (allow a slight curve within 10 % of t₁ ) clear decrease after hitting surface; (allow straight line or concave curve as shown, do not allow convex curve)

constant non-zero speed reached smaller than maximum; (speed must be less than maximum velocity)

Do not penalize answers where a curve is drawn to the dotted lines as there should not be a discontinuity at the two lines. Do not penalize if the line continues to t₂ or zero velocity shown at t₂.

correctly labelled forces;

correct direction and equal lengths; (judge by eye)

Accept co-linear/vector arrows that do not begin at the stone.

Accept arrow heads finalizing at the stone.

Treat mention of upthrust as neutral.

(i) and (ii) These were high scoring questions with a substantial number of correct solutions. Even those who could not answer (i) were able to take their incorrect value and use it correctly in (ii).

This part was not straightforward and demands some thought by candidates – ideally before they put pen to paper. A number of candidates achieved two marks. Common faults included: setting the final speed in the water at higher than the final speed in air; a significantly curved first section before t₁; incorrect curvature between t₁ and t₂ and lack of a final constant speed or a zero final speed.

This straightforward question was not well done. Many candidates did not draw two clear lines of appropriate length with a ruler – crude, free-hand sketches were very common. The question asks for labelling and this should be done with words, not symbols. Mention of up thrust was not required in the answer, although its inclusion was treated as neutral.