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.

Photo AI

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

96%

114 rated

Answer

To find the final speed (v) when the diver reaches the surface of the pool, we can use the equation of motion:

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

where:

$u = 4 \, \text{m s}^{-1}$ (initial speed going upwards),
$a = -g = -9.8 \, \text{m s}^{-2}$ (acceleration due to gravity, acting downwards),
$s = -5 \, \text{m}$ (the distance fallen, negative because she is moving downwards).

Substituting in the values gives:

$v^2 = (4)^2 + 2(-9.8)(-5)$

Calculating we get:

$v^2 = 16 + 98 = 114 \Rightarrow v = \sqrt{114} \approx 10.7 \, \text{m s}^{-1}$

Thus, her speed when she reaches the surface of the pool is approximately 10.7 m s⁻¹.

Step 2

the time taken to reach the surface of the pool

99%

104 rated

Answer

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

$v = u + at$

Rearranging for t gives:

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

Substituting in the values, where we already calculated v:

$u = 4 \, \text{m s}^{-1}$ ,
$a = -g = -9.8 \, \text{m s}^{-2}$ ,
$v = 10.7 \, \text{m s}^{-1}$ (the value calculated previously).

This gives:

$t = \frac{10.7 - 4}{-9.8} = \frac{6.7}{-9.8} \approx 1.5 \, \text{s}$

Thus, the time taken to reach the surface of the pool is approximately 1.5 seconds.

Step 3

State two physical factors which have been ignored in the model

96%

101 rated

Answer

Two physical factors that have been ignored in the model are:

Air resistance, which would act against the motion of the diver, reducing her acceleration.
The spin of the diver, which could affect her orientation and speed during the dive.

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

Join the A-Level students using SimpleStudy...