Determine the position of an object in projectile motion

Solved problems in projectile motiondetermine the position of an object

1. A body is projected upward at an angle of 60o to the horizontal with an initial speed of 12 m/s. Determine the position of the object after moving for 1 second! Acceleration of gravity is 10 m/s2.

Known :

Angle (θ) = 60o

Initial velocity (vo) = 12 m/s

Time interval (t) = 1 second

Acceleration of gravity (g) = 10 m/s2

Wanted : Object position after moving during 1 second

Solution :

Solving projectile motion problems – determine the position of an object 1Horizontal component of initial velocity :

vox = vo cos θ = (12 m/s)(cos 60o) = (12 m/s)(0.5) = 6 m/s

Vertical component of initial velocity :

voy = vo sin θ = (12 m/s)(sin 60o) = (12 m/s)(0.53) = 63 m/s

Object position at horizontal direction:

Known :

Horizontal component of velocity (vx) = 6 m/s

Time interval (t) = 1 second

Wanted : horizontal range (x)

Solution :

6 meters / second means the ball moves as far as 6 meters every 1 second. The distance of the ball after moving for 1 second is 6 meters. So the position of the ball in the horizontal direction is 6 meters.

Object position at vertical direction :

Choose upward direction as positive and downward direction as negative.

Known :

Initial velocity (vo) = 63 m/s (positive upward)

Time interval (t) = 1 second

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

Wanted : height after moving during 1 second

Solution :

h = vo t + 1/2 g t2 = (63)(1) + 1/2 (-10)(12) = 63 + (-5)(1) = 63 – 5 = 6(1.7) – 5 = 10.2 – 5 = 5.2 meters.

Object position after moving for 1 second :

Horizontal displacement (x) = 6 meters

Vertical displacement (y) = 5.2 meters

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2. A body is projected upward at an angle of 30o to the horizontal from a building 20 meters high. Its initial speed is 50 m/s. Calculate the vertical displacement after the body moving for 1 second! Acceleration of gravity is 10 m/s2.

Known :

Angle (θ) = 30o

Initial height (ho) = 20 meters

Initial velocity (vo) = 50 m/s

Time interval (t) = 1 second

Acceleration of gravity (g) = 10 m/s2

Wanted : Height (h)

Solution :

Vertical component of initial velocity :

voy = vo sin θ = (50 m/s)(sin 30o) = (50 m/s)(0.5) = 25 m/s

Height :

Choose upward direction as positive and downward direction as negative.

Known :

Initial velocity (vo) = 25 m/s (positive upward)

Time interval (t) = 1 second

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

Wanted : Height (h)

Solution :

h = vo t + 1/2 g t2 = (25)(1) + 1/2 (-10)(12) = 25 + (-5)(1) = 25 – 5 = 20 meters.

The height of the body after moving for 1 second is 20 meters above where the body is projected or 40 meters above ground.

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3. A small ball projected horizontally with initial velocity vo = 10 m/s from a building 10 meters high. Calculate the ball displacement after moving 1 second! Acceleration of gravity is 10 m/s2

Known :

Initial height (h) = 10 meters

Initial velocity (vo) = 10 m/s

Time interval (t) = 1 second

Acceleration of gravity (g) = 10 m/s2

Wanted: Position of the ball after moving 1 second!

Solution :

Solving projectile motion problems – determine the position of an object 2Horizontal displacement :

Known :

Horizontal component of velocity (vx) = 10 m/s

Time interval (t) = 1 second

Wanted: Position of the object

Solution :

10 meters/second means the object move as far as 10 meters every 1 second. Displacement after moving for 1 second is 10 meters. So horizontal displacement is 10 meters.

Vertical displacement :

Calculated as the free fall motion.

Known :

Time interval (t) = 1 second

Acceleration of gravity (g) = 10 m/s2

Wanted : Height after moving during 1 second (h)

Solution :

h = 1/2 g t2 = 1/2 (10)(12) = (5)(1) = 5 meters.

After 1 second, the object falls as far as 5 meters. Height above the ground level = 10 meters – 5 meters = 5 meters.

The position of the object after moving 1 second :

Position of the object at horizontal direction (x) = 10 meters

The position of the object at vertical direction (y) = 5 meters

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  1. Resolve initial velocity into horizontal and vertical components
  2. Determine the horizontal displacement
  3. Determine the maximum height
  4. Determine the time interval
  5. Determine the position of the object
  6. Determine the final velocity