A ball is projected vertically upwards with speed 21 m s⁻¹ from a point A, which is 1.5 m above the ground - Edexcel - A-Level Maths Mechanics - Question 5 - 2007 - Paper 1

To calculate the speed of the ball as it reaches the ground, we again use the kinematic equation:

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

Here:

• Initial velocity $u = 0$ m/s at the peak height.
• Final velocity $v$ is what we need to find.
• Acceleration $a = 9.8$ m/s² (downwards).
• Displacement $s = 1.5 + h = 1.5 + 22.5 = 24$ m.

Using the equation: $v^2 = 0 + 2 \times 9.8 \times 24$

Calculating gives: $v = \sqrt{470.4} \approx 22 \text{ m/s}$

To find the total time, we can use the equation:

$v = u + at$

Where:

• Final velocity $v = -v$ (speed downward) as it reaches the ground.
• Initial velocity $u = 21$ m/s.
• Acceleration $a = -9.8$ m/s² (downwards).

Rearranging gives: $t = \frac{v - u}{a}$

Calculating gives: $t = \frac{-\sqrt{470.4} - 21}{-9.8} \approx 4.4 \text{ s}$