Answer to Question #241622 in Physics for jena

Question

Anton claims that he can throw a dart at a dartboard from a distance of 2.0m and hit the 5.0cm-wide bull's eye if he throws the dart horizontally with a speed of 20m/s. He starts the throw at the same height as the top of the bull's eye. Will Anton hit the bull's eye?

(I need complete solution plssss)

Answer 1

First, find the time the required for the dart to pass the distance of 2 m at 20 m/s:

$$t=\frac Dv=0.1\text{ s}.$$

Second, find the vertical displacement the dart will go (because it not only moves horizontally but vertically as well under the influence of gravity, so basically it's addition of two motions: horizontal at 20 m/s and vertical 'falling' during the time t):

$$h=\frac{gt^2}{2}=0.049\text{ m},$$

which is equivalent to 4.9 cm. Therefore, since the target's diameter is 5 cm, Anton will be able to hit the target.