Step-by-step explanation:
(a) Given:
Δy = 0 m
v₀ᵧ = 20.0 m/s sin 53° = 16.0 m/s
aᵧ = -9.8 m/s²
Find: t
Use an equation that doesn't include final velocity, v.
Δy = v₀ᵧ t + ½ aᵧt²
0 m = (16.0 m/s) t + ½ (-9.8 m/s²) t²
0 = 16t − 4.9t²
0 = t (16 − 4.9t)
t = 3.26 s
(b) Given:
v₀ₓ = 20.0 m/s cos 53° = 12.0 m/s
aₓ = 0 m/s²
t = 3.26 s
Find: Δx
Use an equation that doesn't include final velocity, v.
Δx = v₀ₓ t + ½ aₓt²
Δx = (12.0 m/s) (3.26 s) + ½ (0 m/s²) (3.26 s)²
Δx = 39.24 m
(c) Given:
v₀ᵧ = 20.0 m/s sin 53° = 16.0 m/s
vᵧ = 0 m/s
aᵧ = -9.8 m/s²
Find: Δy
Use an equation that doesn't include t.
vᵧ² = v₀ᵧ² + 2aᵧ Δy
(0 m/s)² = (16.0 m/s)² + 2 (-9.8 m/s²) Δy
Δy = 13.02 m
Alternatively, use t/2 = 1.63 seconds, and use an equation that doesn't include the final velocity, v.
Δy = v₀ᵧ t + ½ aᵧt²
Δy = (16.0 m/s) (1.63 s) + ½ (-9.8 m/s²) (1.63 s)²
Δy = 13.02 m