A competitor makes a dive from a high springboard into a diving pool. She leaves the springboard vertically with a speed of 4 m s⁻¹ upwards. When she leaves the springboard, she is 5 m above the surface of the pool. The diver is modelled as a particle moving vertically under gravity alone and it is assumed that she does not hit the springboard as she descends. Find (a) her speed when she reaches the surface of the pool, (b) the time taken to reach the surface of the pool. (c) State two physical factors which have been ignored in the model.

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A competitor makes a dive from a high springboard into a diving pool - Edexcel - A-Level Maths Mechanics - Question 3 - 2003 - Paper 1

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A competitor makes a dive from a high springboard into a diving pool. She leaves the springboard vertically with a speed of 4 m s⁻¹ upwards. When she leaves the spri... show full transcript

Worked Solution & Example Answer:A competitor makes a dive from a high springboard into a diving pool - Edexcel - A-Level Maths Mechanics - Question 3 - 2003 - Paper 1

Step 1

(a) her speed when she reaches the surface of the pool

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Answer

To find the speed when the diver reaches the surface of the pool, we can use the kinematic equation:

$v^2 = u^2 + 2as$

where:

$v$ = final velocity
$u$ = initial velocity = 4 m/s
$a$ = acceleration due to gravity = -9.81 m/s² (downwards)
$s$ = distance = -5 m (the diver is moving downwards to the surface of the water).

Substituting the known values, we have:

$v^2 = (4)^2 + 2(-9.81)(-5)$
$v^2 = 16 + 98.1$
$v^2 = 114.1$
Thus, $v = ext{sqrt}(114.1) \approx 10.7 m/s$
Therefore, her speed when she reaches the surface of the pool is approximately 10.7 m/s.

Step 2

(b) the time taken to reach the surface of the pool

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Answer

To find the time taken to reach the surface of the pool, we can use the equation:

$v = u + at$
Rearranging for time ( $t$ ), we get: $t = \frac{v - u}{a}$

Using the values we have:

$u = 4$ m/s (initial speed),
$v \approx 10.7$ m/s (final speed from part (a)),
$a = -9.81$ m/s² (acceleration).

Substituting: $t = \frac{10.7 - 4}{-9.81}$
$t \approx \frac{6.7}{9.81} \approx 0.683 s$
Thus, the time taken to reach the surface of the pool is approximately 0.683 seconds.

Step 3

(c) State two physical factors which have been ignored in the model

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Answer

Air resistance: The effect of air friction on the diver's motion is not accounted for in the model, which would generally slow the diver down.
Spin: The possible rotational movement of the diver, which could affect her trajectory and speed upon entering the water, is ignored.

A competitor makes a dive from a high springboard into a diving pool - Edexcel - A-Level Maths Mechanics - Question 3 - 2003 - Paper 1

Worked Solution & Example Answer:A competitor makes a dive from a high springboard into a diving pool - Edexcel - A-Level Maths Mechanics - Question 3 - 2003 - Paper 1

(a) her speed when she reaches the surface of the pool

(b) the time taken to reach the surface of the pool

(c) State two physical factors which have been ignored in the model

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