A ball thrown vertically upward… | Physics

Question 1 Report

A ball thrown vertically upward reaches a maximum height of 50 m above the level of projection. Calculate the;

(i) time taken to reach the maximum height,

(ii) speed of the throw. [g = 10 ms\(^{-2}\)]

Answer

Answer Details

Given: maximum height \(h = 50\ \text{m}\), \(g = 10\ \text{m s}^{-2}\), and velocity at the top \(= 0\).

(ii) Speed of throw (find first): using \(v^{2} = u^{2} - 2gh\) with \(v = 0\):

\[ 0 = u^{2} - 2(10)(50) \Rightarrow u^{2} = 1000 \] \[ u = \sqrt{1000} = 31.6\ \text{m s}^{-1} \]

(i) Time to reach maximum height: using \(v = u - gt\) with \(v = 0\):

\[ t = \frac{u}{g} = \frac{31.6}{10} = 3.16\ \text{s} \]

The ball takes about 3.16 s to reach the top, having been thrown at about 31.6 m s\(^{-1}\).

A ball thrown vertically upward reaches a maximum height of 50 m above the level of projection. Calculate the; (i) time taken to reach the maximum height, (...