Answer:
tair = 11.5 s
vi = 60.3 m/s
Step-by-step explanation:
In the x direction:
Given:
x₀ = 0 m
x = 600 m
v₀ = v cos 30° = v √3/2
a = 0 m/s²
x = x₀ + v₀ t + ½ at²
600 = 0 + (v √3/2) t + ½ (0) t²
600 = √3/2 v t
1200/√3 = v t
In the y direction:
Given:
y₀ = 300 m
y = 0 m
v₀ = v sin 30° = v/2
a = -9.8 m/s²
y = y₀ + v₀ t + ½ at²
0 = 300 + (v/2) t + ½ (-9.8) t²
0 = 300 + 1/2 v t − 4.9t²
Substitute:
0 = 300 + 1/2 (1200/√3) − 4.9t²
0 = 300 + 600/√3 − 4.9t²
4.9t² = 300 + 600/√3
t = 11.5 s
Solve for v:
v t = 1200/√3
v = 60.3 m/s
Graph:
desmos.com/calculator/1syounu0cg