2. In 1971, astronaut Allen Shepard hit a golf ball on the moon, the path of a golf ball hit at an angle of 45 degrees and with a speed of 100ft per second can be modeled by
g
y= - ----------xsquared( 2 ) + x
10,000
where x is the ball's horizontal position (in feet), y is the corresponding height(in feet) and g is the acceleration due to gravity (in feet per seconds squared).
10
To understand the equation and how to model the path of the golf ball, let's break it down:
1. The equation represents the height (y) of the golf ball as a function of its horizontal position (x) on the moon's surface.
2. The equation starts with the term "g/10,000." Here, "g" represents the acceleration due to gravity, and "10,000" is a constant. Dividing "g" by "10,000" scales down the effect of gravity on the moon compared to Earth.
3. The next term is "-x^2(2)." This term represents the horizontal position (x) of the ball squared and then multiplied by -2. Squaring x ensures that it is always positive, and multiplying it by -2 creates a downward-opening parabolic shape for the trajectory of the ball.
4. Finally, we have "+x" at the end of the equation. This term represents the horizontal position (x) of the ball itself. It is included to shift the parabolic curve horizontally, ensuring that the ball starts at the correct position.
By using this equation, we can calculate the height (y) of the golf ball at any given horizontal position (x), following a parabolic path until it reaches the maximum height and then descends back to the surface.
If you want to calculate the height of the ball at a specific horizontal position using this equation, you would substitute the desired value of "x" into the equation and solve for "y."