a missile is moving 1810 m/s at a 20.0. It needs to hit a target 29,500m away in a 65.0 magnitude in 9.20s. What acceleration must its engine produce?

323 m/s²

Explanation:

Given:

x₀ = 0 m

y₀ = 0 m

x = 29500 cos 65°

y = 29500 sin 65°

v₀x = 1810 cos 20°

v₀y = 1810 sin 20°

t = 9.20

Find:

ax, ay, θ

First, in the x direction:

x = x₀ + v₀ t + ½ at²

29500 cos 32° = 0 + (1810 cos 20°) (9.20) + ½ ax (9.20) ²

25017 = 15648 + 42.32 ax

ax ≈ 221.4

And in the y direction:

y = y₀ + v₀ t + ½ at²

29500 sin 32° = 0 + (1810 sin 20°) (9.20) + ½ ay (9.20) ²

15633 = 5695 + 42.32 ay

ay ≈ 234.8

Therefore, the magnitude of the acceleration is:

a² = ax² + ay²

a² = (221.4) ² + (234.8) ²

a ≈ 322.7

Rounded to 3 significant figures, the magnitude of the acceleration is approximately 323 m/s².