# Determine final velocity of projectile motion

1. A kicked football leaves the ground at an angle θ = 30o to the horizontal with an initial speed of 14 m/s. Calculate the final velocity before the ball hits the ground.

Known :

Angle (θ) = 3o

o) = 14 m/s

10 m/s2

Wanted : Final velocity before the ball hits the ground

Solution : Horizontal component of initial velocity :

vox = vo cos θ = (14 m/s)(cos 30o) = (14 m/s)(0.53) = 73 m/s

Vertical component of initial velocity :

voy = vo sin θ = (14 m/s)(sin 30o) = (14 m/s)(0.5) = 7 m/s

Final velocity at vertical direction

Choose upward direction as positive and downward direction as negative.

Known :

Initial velocity (vo) = 7 m/s (positive upward)

Acceleration of gravity (g) = –10 m/s2 (negative downward)

Height (h) = 0 (object back to initial position)

Wanted : Final velocity (vt)

Solution :

vt2 = vo2 + 2 g h = 72 + 2(-10)(0) = 49 – 0 = 49

vt = √49 = 7 m/s

Final velocity at horizontal direction

Initial velocity at horizontal direction is 73 m/s. Velocity is constant so that final velocity is same as initial velocity.

Final velocity before the object hits the ground 2. A body is projected upward at an angle of 30o with the horizontal from a building 5 meter high. Its initial speed is 10 m/s. Calculate final velocity before the object hits the ground! Acceleration of gravity is 10 m/s2.

Known :

Angle (θ) = 30o

Initial height (ho) = 5 meters

Initial velocity (vo) = 10 m/s

Acceleration of gravity (g) = 10 m/s2

Wanted : Final velocity

Solution :

Horizontal component of initial velocity :

vox = vo cos θ = (10 m/s)(cos 30o) = (10 m/s)(0.53) = 53 m/s

Vertical component of initial velocity :

voy = vo sin θ = (10 m/s)(sin 30o) = (10 m/s)(0.5) = 5 m/s

Final velocity at vertical direction

Known :

Initial velocity (vo) = 5 m/s (positive upward)

Acceleration of gravity (g) = –10 m/s2 (negative downward)

Height (h) = -5 m (negative because the ground is below the initial height)

Wanted : Final velocity (vt)

Solution :

vt2 = vo2 + 2 g h = 52 + 2(-10)(-5) = 25 + 100 = 125

vt = √125 m/s

Final velocity at horizontal direction

Final velocity at horizontal direction is 5√3 m/s.

Final velocity 3. A small ball projected horizontally with initial velocity vo = 8 m/s from a building 12 meters high. Calculate final velocity before ball hits ground! Acceleration of gravity is 10 m/s2

Known :

Height (h) = 12 meters

Initial velocity (vo) = 8 m/s

Acceleration of gravity (g) = 10 m/s2

Wanted : Final velocity (vt)

Solution : Horizontal component of initial velocity :

vox = vo = 8 m/s

Vertical component of initial velocity :

voy = 0 m/s

Final velocity at vertical direction

calculated using equation of free fall motion.

Known :

Acceleration of gravity (g) = 10 m/s2

Height (h) = 12 m

Wanted : Final velocity (vt)

Solution :

vt2 = 2 g h = 2(10)(12) = 240

vt = √240 m/s

Final velocity at horizontal direction

Initial velocity at the horizontal direction is 8 m/s. Velocity is constant so that the initial velocity equals the final velocity. So final velocity at horizontal direction is 8 m/s.

Final velocity Read :  Simple machine (inclined plane, lever) - problems and solutions