Determine the flight time and heights of 2 balls thrown vertically

In summary, the task involves calculating the flight time and maximum heights of two balls thrown vertically, taking into account factors such as initial velocity, acceleration due to gravity, and the equations of motion. By applying these principles, one can determine how long each ball will be in the air and the peak height it reaches during its trajectory.
  • #1
tremain74
12
3
Homework Statement
Child A throws a ball vertically up with a speed of 10 m/s from the top of a shed 3 meters high. Child B on the ground at the same instant throws a ball vertically up with a speed of 13.5 m/s. Determine the time at which the two balls will be at the same height above the ground. What is the height? The answers were t = 0.857 s and h = 15.17.
Relevant Equations
I used the equations 3 + (10*x) = 13.5*x.
To find the time of this problem, I used the equations 3 + (10 * x ) = 13.5 *x. 3 = 3.5*x. Therefore x was 0.857. To start off with child A was already three feet above ground and I got the answer to the time. However I couldn't find the height.
 
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  • #2
show what work you did do to try to get the height.
 
  • #3
The one formula that I thought about was the projectile motion formula using y = -4.9t^2 + vo*t*sinO. Sin O(sin of theta). However this does not solve my problem to find the correct height.
 
  • #4
Since the balls were thrown vertically, why would you think there would be an angle involved. Do you have ANY experience with projectile motion? It certainly seems as though you do not, so I would suggest you go back and study the basics of projectile motion.
 
  • #5
Surprisingly the OP's answer for the first part is correct albeit using variable x instead of t. This is because in problems like this the quadratic term(s) in the respective motion equations cancel out and one is left with exactly the equation solved by the OP.

The OP also wrote the correct equation to find the height - just needed to replace "vo" with 13.5 m/s. and the angle of projection is 90 degrees if the ball is thrown vertically upward.

The given answer for the height at which the balls meet (are in same horizontal line) seems incorrect - should be 13.5*0.857-4.9*(0.857)^2=7.971 m. See following graph.

https://www.desmos.com/calculator/snmbofcveh
 
Last edited:

FAQ: Determine the flight time and heights of 2 balls thrown vertically

1. How do I determine the flight time of the balls thrown vertically?

To determine the flight time of each ball, you can use the kinematic equation for motion under constant acceleration due to gravity. The formula is: T = (2 * V₀) / g, where T is the total flight time, V₀ is the initial velocity of the ball, and g is the acceleration due to gravity (approximately 9.81 m/s²). The time to reach the highest point is V₀/g, and the total flight time is twice that value.

2. How can I calculate the maximum height reached by each ball?

The maximum height (H) can be calculated using the formula: H = (V₀²) / (2 * g), where V₀ is the initial velocity and g is the acceleration due to gravity. This equation derives from the energy conservation principle, stating that the initial kinetic energy is converted to potential energy at the maximum height.

3. What factors affect the flight time and height of the balls?

The main factors that affect the flight time and height of the balls are the initial velocity at which they are thrown and the acceleration due to gravity. Additionally, air resistance can play a role, but it is often negligible for simple calculations in a vacuum or ideal conditions.

4. If two balls are thrown with different initial velocities, how do their flight times compare?

If two balls are thrown with different initial velocities, the ball with the higher initial velocity will have a longer flight time. The relationship between initial velocity and flight time is linear, meaning that if you double the initial velocity, the flight time will also increase proportionally.

5. Can I use the same formulas for balls thrown at angles instead of vertically?

No, the formulas for flight time and maximum height are specific to vertical motion. When balls are thrown at an angle, you need to separate the motion into horizontal and vertical components. The vertical component can still use the same formulas, but you must consider the angle of projection to calculate the initial vertical velocity (V₀y = V₀ * sin(θ)).

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