Question

An archer shoots an arrow with a speed of 200 ft/s, if the arrow travels 2 ft before being shoot, what was its acceleration (supposing it's constant)? Express in m/s^2... I got -30.78 m/s^2, is that correct?

Answer 1

An archer shoots an arrow with a speed of 200 ft/s, if the arrow travels 2 ft before being shot, what was its acceleration (supposing it's constant)? Express in m/s^2... I got -30.78 m/s^2, is that correct?

Solution:

S = 2ft = 0.61m – distance, that arrow travels before being shot;

V = 61 $\frac{\text{m}}{\text{s}}$ – speed of the arrow;

a – acceleration of the arrow;

t – time before arrow being shot;

The equation of motion for the arrow along the X axis:

$$S = \frac{a t^2}{2}$$

The rate equation for the arrow along the X axis:

$$V = 0 + a t$$ $$t = \frac{V}{a}$$

(2)in(1):

$$S = \frac{a \left(\frac{V}{a}\right)^2}{2} = \frac{V^2}{2a}$$ $$a = \frac{V^2}{2S} = \frac{\left(61 \frac{\text{m}}{\text{s}}\right)^2}{2 \cdot 0.61 \text{m}} = 3050 \frac{\text{m}}{\text{s}^2}.$$

Answer: acceleration of the arrow is $3050 \frac{\text{m}}{\text{s}^2}$.