A punter in a football game kicks a ball from the goal line at 60° from the horizontal at 25 m/s. What is the hang time of the punt?
Compute the time it takes for the vertical velocity component to become zero; then double it for the "hang time". It takes just as long going up as coming down.
To merit honors for your physics class work, you should attempt more of it.
To find the hang time of the punt, we need to determine how long the ball stays in the air. We can use the kinematic equations of motion to solve this problem.
Step 1: Analyze the given information:
- Initial velocity (vi) = 25 m/s
- Launch angle (θ) = 60°
Step 2: Resolve the initial velocity into its vertical and horizontal components:
- The vertical component of the initial velocity (viy) is given by viy = vi * sin(θ)
- The horizontal component of the initial velocity (vix) is given by vix = vi * cos(θ)
Step 3: Calculate the hang time using the vertical component:
- The time (t) it takes for an object to reach its maximum height and return to the same vertical position (hang time) can be calculated using the vertical component of the initial velocity and the acceleration due to gravity.
- The equation to calculate the hang time is t = (2 * viy) / g, where g is the acceleration due to gravity (g = 9.8 m/s²).
Step 4: Substitute the values into the equation and solve for t:
t = (2 * viy) / g
= (2 * (vi * sin(θ))) / g
Now, let's calculate the hang time of the punt:
Substituting the given values:
t = (2 * (25 * sin(60°))) / 9.8
Step 5: Simplify and calculate the answer:
t = (2 * 25 * √3 / 2) / 9.8
= (50 * √3) / 9.8
≈ 3.04 seconds
Therefore, the hang time of the punt is approximately 3.04 seconds.
To find the hang time of the punt, we first need to understand the components of the ball's motion. In this case, we are given the initial velocity of the ball, which is 25 m/s, and the angle at which it is kicked, which is 60° from the horizontal.
The motion of the ball can be broken down into two components: horizontal and vertical. The horizontal component remains constant throughout the motion, while the vertical component is affected by gravity.
To determine the hang time, we need to find the time it takes for the ball to reach its maximum height and then double that time. At the maximum height, the vertical component of the ball's velocity becomes zero.
Let's break down the problem further:
1. Calculate the vertical component of the initial velocity:
Vertical velocity (Vy) = V * sin(angle)
Vy = 25 m/s * sin(60°)
2. Use the formula for the time of flight for an object thrown upwards:
Time of flight = 2 * (Vy / g)
Here, g represents the acceleration due to gravity, which is approximately 9.8 m/s².
3. Calculate the hang time by substituting the values and solving the equation:
Hang time = 2 * (Vy / g)
Now, let's calculate the answer step by step:
1. Calculate the vertical component of the initial velocity:
Vy = 25 m/s * sin(60°)
Vy = 25 m/s * 0.866 (rounding to 3 decimal places)
Vy ≈ 21.650 m/s
2. Determine the time of flight:
Time of flight = 2 * (Vy / g)
Time of flight = 2 * (21.650 m/s / 9.8 m/s²)
Time of flight ≈ 4.426 seconds (rounding to 3 decimal places)
3. Find the hang time:
Hang time = 2 * (Time of flight)
Hang time = 2 * 4.426 s
Hang time ≈ 8.852 seconds (rounding to 3 decimal places)
Therefore, the hang time of the punt is approximately 8.852 seconds.