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.

A-Level Edexcel Maths Mechanics Variable Acceleration - 1D: A competitor makes a dive from a

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

Question 3

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

her speed when she reaches the surface of the pool

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Answer

To calculate her speed when she reaches the surface of the pool, we can use the equation of motion:

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

where:

$v$ = final velocity (speed when reaching the surface),
$u$ = initial velocity = 4 m/s,
$a$ = acceleration due to gravity = -9.81 m/s² (negative as it opposes the initial upward velocity),
$s$ = distance fallen = -5 m (negative since falling down).

Substituting the values, we have:

$v^2 = 4^2 + 2(-9.81)(-5)$

$v^2 = 16 + 98.1$

$v^2 = 114.1$

Taking the square root gives:

$v = ext{sqrt}(114.1) \\ \\ v ≈ 10.7 ext{ m/s}$

Step 2

the time taken to reach the surface of the pool

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Answer

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

$v = u + at$

Rearranging this gives:

$t = \frac{v - u}{a}$

Substituting the known values:

Final velocity ( $v$ ) is 10.7 m/s (calculated),
Initial velocity ( $u$ ) is 4 m/s,
Acceleration ( $a$ ) is -9.81 m/s².

So,

$t = \frac{10.7 - 4}{-9.81}$

Calculating:

$t = \frac{6.7}{9.81} ≈ 0.682 ext{ s}$

Step 3

State two physical factors which have been ignored in the model

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Answer

Air resistance – this would affect the speed of the diver and the time taken to reach the surface.
The spin of the diver – any rotational motion would alter her descent.

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

her speed when she reaches the surface of the pool

the time taken to reach the surface of the pool

State two physical factors which have been ignored in the model

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