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.
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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 − gt
up
t
up
= vᵧ / g
=
s
Step 3: Double for total time of flight
T = 2 × t
up
=
s
Your answer for (a):
Check
Step 4: Find maximum height
h
max
= vᵧ² / (2g)
=
m
Your answer for (b):
Check
Step 5: Find range
R = vₓ × T
=
m
Your answer for (c):
Check
Full Solution:
vₓ = v₀ cos(θ) =
m/s
vᵧ = v₀ sin(θ) =
m/s
t
up
= vᵧ/g =
s
(a) T = 2t
up
=
s
(b) h
max
= vᵧ²/(2g) =
m
(c) R = vₓ·T =
m