Alexis Farias realizes her dream to play golf on the moon. She hits a golf ball with an initial velocity of 23.5m/s at an angle of 35.0 degrees above the horizontal. The acceleration due to gravity on the moon is 1.67m/s^2.

A). How long is the golf ball in the air?
B). How far does Alexis hit the golf ball?

To answer both parts of the question, we need to break down the motion of the golf ball into its horizontal and vertical components.

Let's start with part A) - finding the total time the golf ball is in the air.

The motion in the vertical direction is affected by gravity. We can use the equations of motion to find the time it takes for the ball to reach its peak height and then return back to the ground.

The initial vertical velocity is calculated by multiplying the initial velocity (23.5 m/s) by the sine of the launch angle (35 degrees). So, Vy = 23.5 m/s * sin(35 degrees).

The time it takes for the ball to reach its peak height can be calculated using the equation: t = Vy / g, where g is the acceleration due to gravity on the moon (1.67 m/s^2).

Once the ball reaches the peak height, it starts to fall back to the ground. The total time in the air is twice the time it takes to reach the peak height.

So, the total time the golf ball is in the air, t_total, is calculated as follows:

t_peak = Vy / g
t_total = 2 * t_peak

Now let's move on to part B) - finding how far Alexis hits the golf ball.

The horizontal motion of the golf ball is not affected by gravity. It moves with a constant velocity in the horizontal direction. The initial horizontal velocity can be calculated by multiplying the initial velocity (23.5 m/s) by the cosine of the launch angle (35 degrees). So, Vx = 23.5 m/s * cos(35 degrees).

The distance the golf ball travels, d, can be calculated using the equation: d = Vx * t_total.

Substituting the values we calculated earlier for Vx and t_total, we can find the answer to part B.

I hope this explanation helps you understand how to solve the problem.