Question

A blow dart is fired horizontally from a height of 1.2 meters. If the dart hits a target that is .6m high and 12m away, what is the initial velocity of the dart?

Answer 1

Blow dart is projected from a height of 1.2 m

Dart will hit the target at height 0.6 m

so the vertical displacement of the dart will be 1.2 - 0.6 = 0.6 m

here we can say that in vertical direction kinematics is applied

$y = v_i* t + \frac{1}{2}at^2$

$0.6 = 0 + \frac{1}{2}*9.8*t^2$

$t = 0.35 s$

now we can say that dart will hit the target after t = 0.35 s

so in the same time it will cover the distance 12 m in horizontal direction

so here in order to find the initial speed we can say

$d = v * t$

$12 = v* 0.35$

$v = \frac{12}{0.35}$

$v = 34.3 m/s$

so dart is projected with speed 34.3 m/s in horizontal direction