Final answer:
To find the total time that the golf ball is in the air, we need to consider the vertical and horizontal motion separately. First, we find the time it takes for the ball to reach its maximum height using the vertical motion equation. Then, we find the time it takes for the ball to land using the horizontal motion equation. Finally, we add the two times together to get the total time.
Step-by-step explanation:
To find the total time that the golf ball is in the air, we need to consider the vertical and horizontal motion separately.
First, we can find the time it takes for the ball to reach its maximum height. Using the vertical motion equation y = y0 + v0y*t - (1/2)g*t^2, where y0 is the initial height, v0y is the initial vertical velocity, g is the acceleration due to gravity, and t is the time, we can solve for the time it takes for the ball to reach its maximum height. Since the maximum height is 10 m and the initial vertical velocity is v0*sin(theta), where theta is the launch angle, we can plug in the values and solve for t.
Next, we can find the time it takes for the ball to land. Using the horizontal motion equation x = x0 + v0x*t, where x0 is the initial horizontal position, v0x is the initial horizontal velocity, and t is the time, we can solve for t. Since the initial horizontal velocity is v0*cos(theta), we can plug in the values and solve for t.
Finally, to find the total time that the ball is in the air, we add the time it takes for the ball to reach its maximum height and the time it takes for the ball to land.