How Do You Solve a Kinematics Tennis Ball Problem Using d-v-a-t Formulas?

In summary, the conversation discusses the task of shooting a tennis ball through two hoops located in the same vertical plane. The equations used to solve for the ball's position and velocity are given, and the coefficients a and b are determined in terms of the launch speed, launch angle, and gravitational field strength. The question also asks for the values of v0 and q0 given specific coordinates for the hoops.
  • #1
dragonx47
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Homework Statement


) You are given the task of shooting a tennis ball from ground level through 2 hoops. The two hoops’ centers and the launch site are located in the same vertical plane, and the hoops are oriented perpendicular to the ball’s proposed trajectory and also in a vertical plane.The first hoop has a height y1 and is located at a horizontal distance from the x1 launch site (which is located at x0, y0). The second hoop is located at x2, y2.a) Use the d-v-a-t formulas to eliminate time and solve for the y-position as function of the x-position. In particular, show that y = a x + b x2Identify the quantities a and b in terms of launch speed v0 and launch angle q0, and the gravitational field strength g (which will later take on the value of 10 m/s2).b) Solve for a and b in terms of x1, y1, x2, and y2.c) For the case of y1 = 4.0 m, x1 = 2.0 m and y2 = 3.0 m, x2 = 4.0 m, determine the values of v0 and q0.

Homework Equations


y = Vy*t + .5(g)(t)^2
x = Vx*t
Vx = Vocos(theta)
Vy = Vosin(theta)

The Attempt at a Solution


I've solved the a) part of the question and gotten that the coefficient a = tan(theta) while the coefficient b = g/(2*(Vocos(theta))^2). I'm not sure how to put these two equations in terms of the position coordinates x1, x2, y2, and y1.
 
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  • #2
Are you assuming the ball's trajectory will pass through the centers of the hoops? If so, then you have 3 points, (x0,y0), (x1,y1), and (x2,y2), to solve what appears to be a quadratic form.
Also, since simple ballistic motion is symmetric, you should see that you want the max y value to occur at (x1+x2)/2, so, you should be able to back that out into some requirement for q0 and v0.
 

FAQ: How Do You Solve a Kinematics Tennis Ball Problem Using d-v-a-t Formulas?

1. What is the Kinematics Tennis Ball Problem?

The Kinematics Tennis Ball Problem is a physics problem that involves calculating the motion of a tennis ball that is thrown or hit in the air. It takes into account factors such as the initial velocity, acceleration due to gravity, and air resistance to determine the trajectory of the ball.

2. How is the problem typically presented?

The problem is typically presented as a scenario where a tennis ball is thrown or hit at a certain angle and initial velocity. The goal is to calculate the maximum height the ball reaches, the distance it travels, and the time it takes to reach the ground.

3. What are the key equations used to solve the Kinematics Tennis Ball Problem?

The key equations used are the equations of motion, such as the kinematic equations, which describe the relationship between the initial velocity, final velocity, acceleration, distance, and time. These equations can be derived from the laws of motion and are essential in solving the problem.

4. How does air resistance affect the trajectory of the ball?

Air resistance, also known as drag, affects the trajectory of the ball by slowing it down as it travels through the air. This means that the ball will not travel as far and will reach a lower maximum height compared to a scenario without air resistance.

5. What other factors should be considered when solving the Kinematics Tennis Ball Problem?

Other factors that should be considered include the density of the air, the shape and size of the ball, and the initial spin of the ball. These factors can affect the amount of air resistance and ultimately the trajectory of the ball.

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