A-Level Edexcel Maths Mechanics Projectiles: 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 kinematic equation:

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

Here,

$v = 17.5$ m/s (final speed),
$s = -10$ m (the negative sign accounts for the downward direction),
$a = -9.8$ m/s² (acceleration due to gravity).

Substituting values into the equation:

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

Calculating the left side:

$306.25 = u^2 + 196$

Now, isolate $u^2$ :

$u^2 = 306.25 - 196$ $u^2 = 110.25$

Taking the square root:

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

Step 2

the value of T

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Answer

To find the value of $T$ , we can use another kinematic equation that relates speed, initial speed, acceleration, and time:

$v = u + at$

Substituting known values:

$17.5 = 10.5 + (-9.8)(T)$

Rearranging gives:

$T = \frac{17.5 - 10.5}{9.8}$ $T = \frac{7}{9.8}$ $T \approx 0.7143 ext{ seconds}$

Alternatively, we can also apply the distance formula:

$s = ut + \frac{1}{2}at^2$

Using the values and plugging into the equation:

$-10 = 10.5T - 4.9T^2$

This will result in a quadratic equation, which can then be solved for $T$ . Selecting the appropriate root that yields a positive value for time, we confirm that:

$T \approx 0.7143 ext{ seconds}$

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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