# What is the range of an arrow shot horizontally at 85.3 m/s if it is initially 1.50 m above the ground?

Dec 1, 2015

$47.2 \text{m}$

#### Explanation:

Use the vertical component of motion to get the time of flight:

$s = \frac{1}{2} \text{g} {t}^{2}$

$\therefore {t}^{2} = \frac{2 s}{g} = \frac{2 \times 1.5}{9.8} = 0.306$

$\therefore t = \sqrt{0.306} = 0.55 \text{s}$

The horizontal component of velocity is constant so:

$s = v \times t = 85.3 \times 0.55 = 47.2 \text{m}$