Jan 2006 1. A stone is thrown vertically upwards with speed 16ms^-1 from a point h metres above the ground. The stone hits the ground 4 s later Find (a) the value of h, (3) (b) the speed of the stone as it hits the ground. (3)

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Jan 2006 1. A stone is thrown vertically upwards with speed 16ms^-1 from a point h metres above the ground. The stone hits the ground 4 s later Find (a) the value of h, (3) (b) the speed of the stone as it hits the ground. (3)

Answer 1

## (a) Implementing the given values into the equation, we get: \[ h = (16 m/s * 4 s) + (0.5 * `-9.8 m/s²` * `(4 s)²`) \] \[ h = 64 m - 78.4 m = -14.4 m \] The negative result was expected; it tells us the stone did not hit at level whence was thrown but lower, its absolute value — the actual observable height that equals to 14.4 m projection from the extent from point of throw. ## (b) Indicate already prepared in Step 3 data to our formula: \[ v = 16 m/s - 9.8 m/s²*4 s = -23.2 m/s \] Negative result implies that the stone is currently going downwards — opposite the initial direction, but what matters in this context is a magnitude: speed not velocity — 23.2 m/s.

Answer 2

## Step 1: This problem involves projectile motion, an area of classical mechanics. Our approach will be formed from principles of upward motion and free-fall. ## Step 2: Calculating \( h \) For correctly calculating the height we will use the well-known equation describing vertical motion: ### \[ h = ut + \frac{1}{2}gt^2 \] In this case, \( u \) is the initial velocity (16 m/s), t is the total time (4 s) and \( g \) is acceleration due to gravity (-9.8 m/s² taking down as negative which makes an equation looks cleaner and more symmetric) ## Step 3: Calculating the speed For determining its final speed, we simply use equations defining velocity during upward motion or during free-fall: ### \( v = u+gt \) \( u \) — initial velocity (also 16 m/s), \( g \) — acceleration due to gravity (-9.8 m/s², cause falling down) and the \( t \) — overall 4 seconds it takes.

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Jan 2006 1. A stone is thrown vertically upwards with speed 16ms^-1 from a point h metres above the ground. The stone hits the ground 4 s later Find (a) the value of h, (3) (b) the speed of the stone as it hits the ground. (3)

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