Question

A ball is thrown vertically upward with a speed of 27.9 m/s from a height of 2.0 m. How long does it take to reach its highest point? The acceleration of gravity is 9.81 m/s 2 . Answer in units of How long does the ball take to hit the ground after it reaches its highest point? Answer in units of s

Answer 1

2.84403 seconds

2.91483 seconds

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s²

`v=u+at\\\Rightarrow t=(v-u)/(a)\\\Rightarrow t=(0-27.9)/(-9.81)\\\Rightarrow t=2.84403\ s`

It takes 2.84403 seconds to reach the highest point

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=(0^2-27.9^2)/(2* -9.81)\\\Rightarrow s=39.67431 m`

The ball will travel 39.67431+2 = 41.67431 m while going down to the ground

`s=ut+(1)/(2)at^2\\\Rightarrow 41.71479=0t+(1)/(2)* 9.81* t^2\\\Rightarrow t=\sqrt{(41.67431* 2)/(9.81)}\\\Rightarrow t=2.91483\ s`

The ball takes 2.91483 seconds to hit the ground after it reaches its highest point.