Question

A ball is thrown directly downward with an initial speed of 8.20 m/s, from a height of 30.7 m. After what time interval does it strike the ground?

Answer 1

Given data

*The given speed of the ball is u = 8.20 m/s

*The given height is h = 30.7 m

The formula for the time interval it takes to strike the ground is given by the equation of motion as

`h=ut+(1)/(2)gt^2`

*Here g is the acceleration due to gravity.

Substitute the known values in the above expression as

`\begin{gathered} 30.7=8.20t+(1)/(2)(9.8)t^2 \\ 30.7=8.20t+4.9t^2 \\ 4.9t^2+8.20t-30.7=0 \\ t=1.80\text{ s} \end{gathered}`

Hence, the time interval it takes to strike the ground is t = 1.80 s