Question

Can you help me resolve this using the quadratic formula?

Answer 1

Answer:

a) Time taken to hit the ground = 1.674 seconds

b) Height at 1 second = 12 m

Step-by-step explanation:

The equation representing the height of the water balloon after t seconds is:

`h(t)=-16t^2+25t+3`

a) At the ground, h(t) = 0

`\begin{gathered} 0=-16t^2+25t+3 \\ \\ 16t^2-25t-3=0 \\ \\ Using\text{ the quadratic formula} \\ t=(-(-25)\pm√((-25)^2-4(16)(-3)))/(2(16)) \\ \\ t=(25\pm√(817))/(32) \\ \\ t=-0.111975,\text{ 1.67448} \end{gathered}`

Since time cannot be negative:

Time taken to hit the ground = 1.674 seconds

b) Height at t = 1 second

`\begin{gathered} H(t)=-16t^2+25t+3 \\ \\ H(1)=-16(1^2)+25(1)+3 \\ \\ H(1)=-16+25+3 \\ \\ H(1)=12\text{ m} \end{gathered}`

Height at 1 second = 12 m