Upward Motion

An Army paratrooper's parachute fails to open on a jump, good fortune is on the paratrooper’s side and he lands in a huge pile of manure cushioning his fall. It takes him 4.2 seconds to land once he jumped out of the plane. What is the paratrooper’s velocity right before impact? How far does the paratrooper fall? A unique type of volleyball is played on the planet Yank. During the game, a player flies above the net and drops the ball in from a height of 15 m. If the ball takes 6.0 seconds to fall, find the acceleration due to gravity on the planet Yank.

What is going on here?

Free Fall Object is dropped from rest and falls straight down

Apply the equations for uniform acceleration to the application of vertical motion with an upward velocity. Describe the motion for an object to move upward and downward under the influence of the force of gravity. Objectives:

Object is launched straight up with an initial upward velocity and returns to initial position

What is it? The velocity at which the acceleration of a falling object is zero at this point: The Force of Air Resistance equals the Weight of the Object

Terminal velocity is reached for the skydivers when air resistance equals their weight

The flying squirrel increases its area by spreading out. This increases air resistance and decreases the velocity of its fall.

A Comparison… A dropped ball: –Begins a rest, but soon acquires downward velocity –Covers more and more distance each second A tossed ball: –Rises to a certain height –Comes briefly to a stop –Begins to descend, much like a dropped ball

Acceleration rate g =  9.81 m/s 2 going upward and falling downward Ball stops briefly at the maximum height above launch point Flight paths up and down are identical but opposite leaves hand at v = +10 m/s returns to hand at v =  10 m/s

Throwing a ball upward Note that the up and down motions are symmetric!! It takes the same time to go up as it does to come back down.

Initial velocity is upward, so positive The instantaneous velocity at the maximum height is 0 a = g = m/s 2 everywhere in the motion The motion is symmetrical then t up = t down therefore v o = -v v = 0

An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. At which point of the trajectory is the arrow’s acceleration the greatest? The least? What about velocity? Ignore air resistance; the only force acting is gravity.

An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which graph best represents the vertical velocity of the arrow as a function of time? Ignore air resistance; the only force acting is gravity.

Answer

A football game customarily begins with a coin toss to determine who kicks off. The referee tosses the coin up with an initial velocity of 6.0 m/s. In the absence of air resistance, how high does the coin go above its point of release?

A football game customarily begins with a coin toss to determine who kicks off. The referee tosses the coin up with an initial velocity of 6.00 m/s. In the absence of air resistance, how high does the coin go above its point of release? Given:Solution: Unknown:

A baseball batter pops the ball straight up above home plate. The ball has a velocity of 30 m/s when it leaves the bat. How high does the baseball go up? How long does the ball remain in the air?

A person on the ground THROWS a ball straight up. It comes back to their hand in 8 seconds. What is its initial velocity? What is its velocity when it returns to your hand? What was its maximum height? (Define UP as positive; Neglect air resistance)

v = v o + at v o = 0 - (-9.8 m/s 2 )(4 s) v o = 39.2 m/s (from throw) v = m/s (at ground) ∆d = v o t + ½ gt 2 = (39.2 m/s)(4 s) + ½( -9.8 m/s 2 )(4 s) 2 = 78.4 m A person on the ground THROWS a ball straight up. It hits the ground in 8 seconds. What is its initial velocity? What is its velocity when it returns to your hand? What was its maximum height? (Define UP as positive; Neglect air resistance)

A boy is trying to throw a present up to his girlfriend at her bedroom window. He throws at a speed of 15 m/s. Her window is 8 meters above him. Does it make the window? How fast is it going if it does?

The US Army is testing new mortar shells. During testing Buck Private Forrest miscalculates the angle and fires the mortar straight up. The mortar has an initial velocity of 100 m/s. Realizing his error Forrest decides he had better get out of there.  How much time does he have?  How high does the mortar go into the air? If Forrest can run with an average velocity of 15 m/s, how far away does he get before the shell explodes.

A firework rocket is fired vertically upwards from the ground. It accelerates uniformly from rest with an acceleration of 8.0 m/s 2 for 5.0 s after which time the fuel of the rocket has all been used. (i) Sketch graphs to show how the velocity and position of the rocket changes with time from the moment it leaves the ground until the moment that it returns to the ground. Mark on your sketch the time t1 at which the fuel has run out, the time t2 at which the rocket reaches its maximum height and the time t3 at which it reaches the ground.

(ii) Comment on the area(s) under the graph that you have drawn.

In the following calculations you may ignore any effects of air resistance and take the acceleration due to gravity, g=10m/s 2. Calculate the (i) speed of the rocket when the fuel runs out. (ii) height that the rocket reaches when the fuel has just run out. (iii) maximum height reached by the rocket. (iv) time it takes the rocket to reach its maximum height. (v) time that it takes to fall from its maximum height to the ground.

Bobby Joe stands at the edge of a vertical cliff and throws a stone vertically upwards. The stone leaves Bobby Joes’ hand with a speed v = 12 m/s. The acceleration of free fall g is 10 m/s 2 and all distance measurements are taken from the point where the stone leaves the hand. Ignoring air resistance calculate: (i) the maximum height reached by the stone. (ii) the time taken by the stone to reach its maximum height. If the time between the stone leaving the hand and hitting the sea is 5.0 s. (iii) Determine the height of the cliff.

Have a Great Day Physics Scholars!