A punter kicks the ball at a 60 degree angle with an initial velocity of 20 m/s. What is its flight-time?
the vertical velocity (vv) is ... 20 m/s * sin(60º)
the flight time is ... 2 * vv / g
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Now, back to your question. Let's tackle it! Since the ball is kicked at a 60-degree angle, we can use some trigonometry to find the vertical component of its initial velocity. The vertical component is given by vₒ * sin(θ), where vₒ is the initial velocity and θ is the angle.
So, the vertical component is 20 m/s * sin(60°) = 20 m/s * √(3)/2 ≈ 17.32 m/s.
Now, we can use the formula for vertical motion to find the flight time. The formula is t = 2 * (vₒy / g), where vₒy is the vertical component of the initial velocity and g is the acceleration due to gravity (approximately 9.8 m/s²).
Plugging in the numbers, we have t = 2 * (17.32 m/s / 9.8 m/s²) ≈ 3.53 seconds.
So, the flight time of the ball is approximately 3.53 seconds. Just enough time for a quick popcorn break!
To find the flight time of the ball, we can use the concepts of projectile motion and the equations of motion. Let's break it down step by step:
Step 1: Identify the known values
- Initial angle (θ) = 60 degrees
- Initial velocity (v₀) = 20 m/s
- Acceleration due to gravity (g) = 9.8 m/s² (assuming we're on the Earth's surface)
Step 2: Resolve the initial velocity into its horizontal and vertical components
The initial velocity can be resolved into two separate components: one in the horizontal direction (v₀x) and one in the vertical direction (v₀y). Since the angle is given, we can use trigonometry to find these components:
v₀x = v₀ * cos(θ)
v₀y = v₀ * sin(θ)
Step 3: Determine the time taken to reach the highest point
The time taken to reach the highest point (t₀) can be found by using the vertical component of the initial velocity and the equation of motion for vertical motion:
v₀y = u + (g * t)
0 = v₀y + (g * t₀)
t₀ = -v₀y / g
Step 4: Calculate the total flight time
The total flight time (t) is equal to twice the time taken to reach the highest point:
t = 2 * t₀
Step 5: Substitute the known values into the equations and calculate the result
Using the values we have:
v₀x = 20 * cos(60°) = 20 * 0.5 = 10 m/s
v₀y = 20 * sin(60°) = 20 * 0.866 = 17.32 m/s
t₀ = -v₀y / g = -17.32 / -9.8 = 1.77 s
t = 2 * t₀ = 2 * 1.77 = 3.54 s
Therefore, the flight time of the ball is approximately 3.54 seconds.