A trackstar in the long jump goes into the jump at 12 meters per second and launches herself at 20 degrees how long is she in the air
To find out how long the trackstar is in the air during the long jump, we need to use the principles of projectile motion. The key is to break down the initial velocity into its horizontal and vertical components.
The initial velocity can be divided into two components: the horizontal component (Vx) and the vertical component (Vy). The horizontal component remains constant throughout the motion, while the vertical component changes due to the influence of gravity.
Given:
Initial velocity (Vi) = 12 m/s
Launch angle (θ) = 20 degrees
First, we need to find the vertical component of the initial velocity (Vy) using trigonometry. We can use the equation:
Vy = Vi * sin(θ)
Vy = 12 m/s * sin(20°)
Vy ≈ 4.09 m/s
Now, we can determine the time of flight (T) using the vertical component (Vy) and the acceleration due to gravity (g).
The equation to calculate the time of flight is:
T = 2 * (Vy / g)
where g is the acceleration due to gravity, approximately 9.8 m/s².
T = 2 * (4.09 m/s / 9.8 m/s²)
T ≈ 0.84 seconds
Therefore, the trackstar spends approximately 0.84 seconds in the air during the long jump.