Answer:
hmax = 211 m
tair = 8.10 s
dx = 210 m
Step-by-step explanation:
In the y direction:
Given:
y₀ = 200 m
v₀ = 30 sin 30° m/s = 15 m/s
a = -9.8 m/s²
Find: y when v = 0 m/s.
v² = v₀² + 2a(y − y₀)
(0 m/s)² = (15 m/s)² + 2 (-9.8 m/s²) (y − 200 m)
y = 211 m
Find: t when y = 0 m.
y = y₀ + v₀ t + ½ at²
(0 m) = (200 m) + (15 m/s) t + ½ (-9.8 m/s²) t²
Solve with quadratic formula:
t = 8.10 s
In the x direction:
Given:
x₀ = 0 m
v₀ = 30 cos 30° m/s = 15√3 m/s
a = 0 m/s²
Find: x when t = 8.10 s.
x = x₀ + v₀ t + ½ at²
x = (0 m) + (15√3 m/s) (8.10 s) + ½ (0 m/s²) (8.10 s)²
x = 210 m
Graph:
desmos.com/calculator/1xawxchikz