Question

A ball is thrown from an initial height of 1 meter with an initial upward velocity of 7 m/s. The balls height h (in meters) after t seconds is given by the following. h=1+7t-5t^2Find all values of t for which the balls height is 2 meters.Round the answer(s) to the nearest hundredth

Answer 1

Solution

To find the values of t for which the ball's height is 2 meters

we set h = 2

=> 2 = 1 + 7t - 5t^2

=>5t^2 - 7t + 1 = 0

Using the quadratic formula,

`\begin{gathered} t=(-b\pm√(b^2-4ac))/(2a) \\ \\ \Rightarrow t=(7\pm√(\left(-7\right)^2-4\left(5\right)\left(1\right)))/(2\cdot5) \\ \\ \Rightarrow t=1.24s\text{ or }0.16s \end{gathered}`

Therefore, t = 1.23s or 0.16s