Learning Objective: Practice solving projectile motion problems step-by-step by resolving components and applying kinematic equations.

Projectile Problem Solver

A ball is kicked at 20 m/s at an angle of 40° above the horizontal. Calculate: (a) time of flight, (b) maximum height, (c) range.
Step 1: Resolve into horizontal and vertical components
vₓ = v₀ cos(θ) and vᵧ = v₀ sin(θ)
vₓ = m/s  |  vᵧ = m/s
Step 2: Find time to reach apex
At apex, vertical velocity is zero: v = u + at → 0 = vᵧ − gtup
tup = vᵧ / g = s
Step 3: Double for total time of flight
T = 2 × tup = s
Step 4: Find maximum height
hmax = vᵧ² / (2g) = m
Step 5: Find range
R = vₓ × T = m
Full Solution:
vₓ = v₀ cos(θ) = m/s
vᵧ = v₀ sin(θ) = m/s
tup = vᵧ/g = s
(a) T = 2tup = s
(b) hmax = vᵧ²/(2g) = m
(c) R = vₓ·T = m