Question

an arrow is launched straight up from the ground with an initial velocity of 23.4 m/s. how long until it reaches its highest point?

Answer 1

Explanation:

Given that,

The initial velocity of an arrow is 23.4 m/s

We need to find the time taken by it to reach its maximum height. Let the maximum height is h.

Using third equation of motion to find height first.

$v^2-u^2=2ah$

At maximum height, v = 0

a = -g

$u^2=2gh\\\\h=\dfrac{u^2}{2g}\\\\h=\dfrac{(23.4)^2}{2\times 9.8}\\\\h=27.93\ m$

Let t is the time to reach its maximum height. So, it can be calculated using second equation motion as follows :

$27.93=23.4t-\dfrac{1}{2}\cdot9.8\cdot t^{2}\\\\t=2.35\ s$

Hence, it will take 2.35 seconds to reach its maximum height.