What formula do I use?

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

c

explanation: