Answer:
a) Time taken to hit the ground = 1.674 seconds
b) Height at 1 second = 12 m
Explanation:
The equation representing the height of the water balloon after t seconds is:
[tex]h(t)=-16t^2+25t+3[/tex]
a) At the ground, h(t) = 0
[tex]\begin{gathered} 0=-16t^2+25t+3 \\ \\ 16t^2-25t-3=0 \\ \\ Using\text{ the quadratic formula} \\ t=\frac{-(-25)\pm\sqrt{(-25)^2-4(16)(-3)}}{2(16)} \\ \\ t=\frac{25\pm\sqrt{817}}{32} \\ \\ t=-0.111975,\text{ 1.67448} \end{gathered}[/tex]
Since time cannot be negative:
Time taken to hit the ground = 1.674 seconds
b) Height at t = 1 second
[tex]\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}[/tex]
Height at 1 second = 12 m
