# How high can a baseball player throw a ball in the air if he can throw it with initial velocity 160 km/h? What would that be standard units?

Dec 14, 2016

$100.68 m$, rounded to two decimal places

#### Explanation:

Initial velocity $u = 160 k m {h}^{-} 1$
Converting in SI units we get $u = 160 \times \frac{1000}{3600} = 44. \overline{4} m {s}^{-} 1$

When the ball is thrown up, assuming vertically, gravity $g = 9.81 m {s}^{-} 2$ will slow it down as it is acting against the direction of motion. At the highest point $h$ the final velocity $v$ will be equal to $0$. Ignoring air friction.
Applicable kinematic equation is
${v}^{2} - {u}^{2} = 2 g h$
Inserting given values we get
${0}^{2} - {\left(44. \overline{4}\right)}^{2} = 2 \times \left(- 9.81\right) \times h$
$\implies h = 100.68 m$, rounded to two decimal places