Question

A dart is thrown horizontally at a speed of 14 m/s at the bull's-eye of a dartboard 4.6 m away, as in the following figure.

(a)

How far below the intended target does the dart hit (in m)?

(b)

What does your answer tell you about how proficient dart players throw their darts?

They aim lower than their intended target.

They aim directly at their intended target.    

They aim higher than their intended target.

Answer 1

(a) Horizontal speed of the dart, v = 14 m/s

time taken by the dart to cover a distance of 4.6 m by the dart -

t = 4.6 / 14 = 0.3286 s.

In this time t, the downward distance covered by the dart due to gravity -

d = u*t + (1/2)*g*t^2 = 0 + 0.5*9.81*0.3286^2 = 0.53 m.

So, the dart will hit 0.53 m below the intended target.

(b) Since when the player aims horiontally target, it hits 0.53 m below the target.

So, for the exact hitting he should aim 0.53 m higher than the intended target.

So, third option is the correct answer.