A man throws ball A downwards with a speed of 2 m s⁻¹ from the edge of a window, 45 m above a dam of water - NSC Physical Sciences - Question 3 - 2016 - Paper 1

Since ball B is thrown one second after ball A, we denote the time for ball A as $t_A$. The time for ball B would then be $t_B = t_A - 1$ s. To calculate the time for ball A, we use:

$\Delta y = v_i t + \frac{1}{2} a t^2$

For ball A: $-45 = 2t_A + \frac{1}{2} (9.8) t_A^2$

This is a quadratic equation in the form: $4.9t_A^2 + 2t_A + 45 = 0$

Using the quadratic formula: $t_A = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ With $a = 4.9$, $b = 2$, and $c = 45$:

Calculating: $t_A = \frac{-2 \pm \sqrt{(2)^2 - 4(4.9)(45)}}{2(4.9)}$

This results in a positive value approximately: $t_A ≈ 2.83s$ Thus, the time for ball B to hit the surface is: $t_B = 2.83 - 1 = 1.83 s$.

To find the initial velocity of ball B, we note that it drops one second after ball A. Since both balls hit the water at the same time and the only variable change is the time of release, we can say:

Since ball A’s total time is $2.83 s$ while ball B’s is $1.83 s$, we can use the same kinematic equation:

$v_f = v_i + at$

For ball B, we have: $29.6 = v_i + (9.8)(1.83)$

Solving for $v_i$ gives: $v_i = 29.6 - (9.8)(1.83)$
$v_i ≈ 15.62 m/s$.

The graph will have time on the x-axis and velocity on the y-axis. For ball A, the initial velocity is 2 m/s and it accelerates downwards due to gravity, leading to a straight line with a positive slope.

For ball B, its initial velocity is determined to be about 15.62 m/s and it also accelerates downwards but starts one second later. The graph for ball B will start at time 1s on the x-axis with a higher initial velocity compared to ball A.

Features to indicate on the graph:

• Mark the initial velocities at the respective time points.
• Indicate that both lines intersect at the point where they hit the water,
• Clearly label time at which ball B is released (t = 1s) and when both balls reach the water.

For clearer illustration, ensure the y-values indicate their respective velocities at their points of intersection.