Question
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
4.2
(236 Votes)
Vernon
Professional · Tutor for 6 years
Answer
## (a)Implementing the given values into the equation, we get:
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:
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.
Explanation
## 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
For correctly calculating the height we will use the well-known equation describing vertical motion:###
In this case,
is the initial velocity (16 m/s), t is the total time (4 s) and
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: ###
— initial velocity (also 16 m/s),
— acceleration due to gravity (-9.8 m/s², cause falling down) and the
— overall 4 seconds it takes.