A-Level Edexcel Maths Mechanics Constant Acceleration - 1D: At time t = 0, a particle is pro

At time t = 0, a particle is projected vertically upwards with speed u m s⁻¹ from a point 10 m above the ground - Edexcel - A-Level Maths Mechanics - Question 2 - 2008 - Paper 1

Question 2

At-time-t-=-0,-a-particle-is-projected-vertically-upwards-with-speed-u-m-s⁻¹-from-a-point-10-m-above-the-ground-Edexcel-A-Level Maths Mechanics-Question 2-2008-Paper 1.png

At time t = 0, a particle is projected vertically upwards with speed u m s⁻¹ from a point 10 m above the ground. At time T seconds, the particle hits the ground with... show full transcript

Worked Solution & Example Answer:At time t = 0, a particle is projected vertically upwards with speed u m s⁻¹ from a point 10 m above the ground - Edexcel - A-Level Maths Mechanics - Question 2 - 2008 - Paper 1

Step 1

the value of u

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Answer

To find the value of u, we can use the equation of motion:

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

Where:

Final velocity, v = 17.5 m/s (downwards, hence taken as negative)
Initial velocity, u = ?
Acceleration, a = -9.8 m/s² (due to gravity)
Displacement, s = -10 m (the particle is falling to the ground)

Substituting these values into the equation:

$(-17.5)^2 = u^2 + 2(-9.8)(-10)$

Calculating the left side:

$306.25 = u^2 + 196$

Now, rearranging the equation:

$u^2 = 306.25 - 196$

$u^2 = 110.25$

Taking the square root gives:

$u = ext{sqrt}(110.25) = 10.5 ext{ m/s}$

Step 2

the value of T

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Answer

For part (b), we can again use the equation of motion:

$v = u + at$

Here:

Final velocity, v = -17.5 m/s
Initial velocity, u = 10.5 m/s
Acceleration, a = -9.8 m/s²
Time, T = ?

Substituting these values into the equation:

$-17.5 = 10.5 - 9.8T$

Rearranging gives:

$-17.5 - 10.5 = -9.8T$

$-28 = -9.8T$

Dividing both sides by -9.8:

$T = rac{28}{9.8}$

Calculating gives:

$T ext{ approximately equals } 2.857 ext{ seconds (or } rac{20}{7} ext{ seconds)}$

At time t = 0, a particle is projected vertically upwards with speed u m s⁻¹ from a point 10 m above the ground - Edexcel - A-Level Maths Mechanics - Question 2 - 2008 - Paper 1

Worked Solution & Example Answer:At time t = 0, a particle is projected vertically upwards with speed u m s⁻¹ from a point 10 m above the ground - Edexcel - A-Level Maths Mechanics - Question 2 - 2008 - Paper 1

the value of u

the value of T

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