Height of plateau form launch speed and angle

Question

A projectile is launched with a speed of 40 m/s at an angle of 30° above the horizontal, as shown in the figure below. The projectile lands on a plateau 3 s later. The height Δy of a plateau is near

A) 15

B) 30

C) 45

Answer 1

The vertical component of the projectile’s initial velocity

v_y0 = v₀ sin(30°) = 40 m/s · 0.5 = 20 m/s

Three seconds later the vertical displacement of the projectile Δy will be

Δy = 20 m/s · 3 s - ¹/₂ ⋅ 10 m/s² ⋅ (3 s)² = 15 m