A golfer, standing on a fairway, hits a shot to a green that is elevated 4.72 m above where she is standing. If the ball leaves her club with a velocity of 49.0 m/s at an angle of 42.5 ° above the ground, find the time that the ball is in the air before it hits the green.
To find the time that the ball is in the air before it hits the green, you can use the equations of motion for projectile motion. The key information you need is the initial velocity of the ball and the angle at which it was hit.
1. Break down the initial velocity into its horizontal and vertical components. The horizontal component (Vx) remains constant throughout the motion, while the vertical component (Vy) is influenced by gravity.
Vx = V * cos(θ)
Vy = V * sin(θ)
In this case, the initial velocity (V) is 49.0 m/s and the angle (θ) is 42.5°.
2. Determine the time it takes for the ball to reach its highest point. At the highest point, the vertical velocity becomes zero (Vy = 0).
The time to reach the highest point (t_max) can be determined using the equation:
Vy = Vy0 + (-g) * t
0 = V * sin(θ) - g * t_max
In this equation, g is the acceleration due to gravity (approximately 9.8 m/s^2).
3. Determine the time it takes for the ball to return to the ground, starting from the highest point.
The total time of flight (t_total) is double the time it takes to reach the highest point (t_max). The time to reach the ground starting from the highest point is the same as the time to reach the highest point.
t_total = 2 * t_max
4. Add the time it takes for the ball to reach the highest point (t_max) to half of the total time of flight (t_total/2) to find the time the ball is in the air before it hits the green.
T = t_max + t_total/2
Now you can substitute the values you have into the equations to find the result.