Solution
- The equation of the path is:
[tex]h(t)=h_0+23t-4.9t^2[/tex]
- When the projectile hits the ground, the height of the projectile, i.e. h(t) = 0.
- We are told that the time when the projectile is on the ground is 5 seconds.
- Thus, when t = 5, h(t) = 0.
- We can use this information to solve the question as follows:
[tex]\begin{gathered} h(t)=h_0+23t-4.9t^2 \\ put\text{ }h(t)=0,t=5 \\ \\ 0=h_0+23(5)-4.9(5)^2 \\ 0=h_0+115-122.5 \\ 0=h_0-7.5 \\ \text{ Add 7.5 to both sides} \\ \\ \therefore h_0=7.5 \end{gathered}[/tex]
Final Answer
The answer is 7.5 meters
