What Are the Peak Height and Total Airtime of a Tennis Ball Thrown Vertically?

In summary, a tennis ball is thrown straight up with an initial speed of 25.0 m/s and caught at the same distance above the ground. The ball reaches a maximum height of approximately 31.888 meters and remains in the air for a total time of approximately 5.102 seconds. The equations used to calculate these values are T=(Vf-Vi)/A and Dy=Vi(sin(90))t+1/2at^2, where T represents time, Vf represents final velocity, Vi represents initial velocity, A represents acceleration, Dy represents change in vertical distance, and t represents time.
  • #1
fparks
1
0

Homework Statement


A tennis ball is thrown straight up with an initial speed of 25.0 m/s. It is caught at the same distance above the ground.

(a) How high does the ball rise?
_________m

(b) How long does the ball remain in the air? (Hint: The time it takes the ball to rise equals the time it takes to fall.)
_________s


Homework Equations





The Attempt at a Solution


i have no idea how to do this. please help!
 
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  • #2
here's your first equation:
T-time Vf-final velocity
Vi-initial velocity A-acceleration
T=(Vf-Vi)/A
the object is going up, so all Velocity is up (no horizontal motion)
vertical acceleration is always -9.8 (due to gravity)
Vi=25m/s, and Vf is 0 at the top (where max vertical distance is reached) so,
T=(0-25)/-9.8 OR T=25/9.8 <(T for max height)
simple multiply by two, and you have your answer for number 3.

your second equation would be:
Dy-change in y distance (vertical), T, Vi, A, and angle (90)
Dy=Vi(sin(90))t+1/2at^2 so,
Dy=25(1)t-4.9t^2 OR Dy=25(25/9.8)-4.9(25/9.8)^2

therefore, T~5.102 <(total T) and Dy~31.888m
where ~ means approximately equal to
 

Related to What Are the Peak Height and Total Airtime of a Tennis Ball Thrown Vertically?

What is the concept of motion in physics?

Motion in physics refers to the change in position of an object over time. It involves the study of how objects move, the factors that affect their motion, and the laws that govern their movement.

What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of both the speed and direction of an object's motion. In other words, velocity takes into account the direction of movement while speed does not.

What is the relationship between acceleration and force?

Acceleration is directly proportional to the net force acting on an object. This means that if the force acting on an object increases, its acceleration will also increase. Similarly, if the force decreases, the acceleration will also decrease.

What are the three laws of motion?

The three laws of motion were developed by Sir Isaac Newton and they are: 1) An object at rest will remain at rest and an object in motion will continue in motion with constant velocity unless acted upon by an external force; 2) The force acting on an object is equal to its mass times its acceleration (F=ma); and 3) For every action, there is an equal and opposite reaction.

What is the difference between uniform and non-uniform motion?

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