A football player kicks a field goal, launchingthe ball at an angle of 48" above the horizontal. During the kick, the ball is in contact with the player's foot for 0.045 s, and the ball's acceleration is 290 m/sz. Vvhat is the range of the football?
Thank you!
search "horizontal range formula"
launch velocity is ... 0.045 * 290
(13.05*sin(48)*2)/9.8=1.97 Is this correct?
sorry 13.05^2
try this ... [13.05^2 * sin(48 * 2)] / 9.8
Got it, thank you very much.
To find the range of the football, we need to calculate the horizontal distance it travels.
First, let's break down the given information:
Angle of launch (θ) = 48° (above the horizontal)
Contact time with the foot (Δt) = 0.045 s
Acceleration (a) = 290 m/s²
The range (R) can be determined using the following equation:
R = V₀x * Δt
Where:
V₀x = initial horizontal velocity
To find V₀x, we need to decompose the initial velocity (V₀) of the ball into its horizontal and vertical components.
The horizontal component (V₀x) remains constant throughout the flight since there is no horizontal acceleration involved. It can be calculated using the following equation:
V₀x = V₀ * cos(θ)
Where:
V₀ = initial velocity of the ball
cos(θ) = cosine of the launch angle
To find V₀, we need to calculate it using the following equation:
V₀ = a * Δt + Vfy
Where:
Vfy = final vertical velocity
To find Vfy, we need to calculate it using the following equation:
Vfy = (a * Δt) + V₀y
Where:
V₀y = initial vertical velocity
Now, we know that the vertical acceleration (ay) is due to gravity and is equal to -9.8 m/s² (downwards). In this case, the ball starts at its highest point and lands at the same level, so the initial and final vertical velocities will be opposite in magnitude but the same in value (V₀y = -Vfy).
Using the above information, we can solve for V₀y:
V₀y = -Vfy = -a * Δt
Now, we can substitute V₀y and Δt in the equation V₀ = a * Δt + V₀y:
V₀ = a * Δt + (-a * Δt)
V₀ = 0
Since the initial velocity (V₀) is 0, the horizontal component of the initial velocity (V₀x) will also be 0:
V₀x = V₀ * cos(θ) = 0 * cos(48°) = 0
Therefore, the range of the football (R) will be 0 meters.