Final answer:
To find the value of g (acceleration due to gravity), use the equation of motion for vertical displacement. Plug in the known values of initial speed and angle of elevation, calculate the initial vertical velocity, and substitute the values into the equation to find g.
Step-by-step explanation:
To find the value of g (acceleration due to gravity), we can use the known information about the projectile: initial speed (V₀ = 230 m/s) and angle of elevation (θ = 60°). The vertical component of the initial velocity is given by V₀y = V₀ * sin(θ). The acceleration due to gravity is equal to the acceleration in the vertical direction, so we can use the equation of motion for vertical displacement:
Δy = V₀yt - (1/2)gt²
Where Δy is the vertical displacement, V₀yt is the initial vertical velocity multiplied by time, and g is the acceleration due to gravity. Rearranging the equation and plugging in the known values, we can solve for g:
g = (2Δy - V₀yt) / t²
Using the given initial speed and angle of elevation, we can calculate the initial vertical velocity as follows:
V₀y = V₀ * sin(θ)
Finally, substituting the values of Δy, V₀y, and t into the equation, we can find the value of g:
g = (2Δy - V₀y * t) / t²
Plugging in the given values and solving the equation should give the value of g.