Find the range at an arrow that leaves a bow at 45 m/s at an angle of 50 degrees above the horizontal level.
R = vo^2 sin 2(theta)/g
To find the range of an arrow that leaves a bow at a given initial velocity and angle, you can use the basic principles of projectile motion. The range is defined as the horizontal distance covered by the projectile before it hits the ground.
The range (R) can be determined using the following formula:
R = (v² * sin(2θ)) / g
Where:
- R is the range
- v is the initial velocity of the arrow (45 m/s in this case)
- θ is the launch angle (50 degrees in this case)
- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)
Let's substitute the values into the equation and calculate the range:
R = (45² * sin(2 * 50)) / 9.8
First, calculate the value of sin(2 * 50):
sin(2 * 50) = sin(100)
sin(100) ≈ 0.9848
Now, substitute the values and calculate the range:
R = (45² * 0.9848) / 9.8
R ≈ (2025 * 0.9848) / 9.8
R ≈ 1987.61 / 9.8
R ≈ 202.82 meters
Therefore, the range of the arrow is approximately 202.82 meters.