B Parametric Equations- Ball travel

[opus]

Suppose a baseball is hit 3 feet above the ground, and that it leaves the bat at a speed of 100 miles an hour at an angle of 20° from the horizontal.

I've got the parametric equations in terms of x and in terms of y, and I have values plotted and a graph sketched. My question is in regards to the initial height of 3 ft, and the position of the ball when it hits the ground. Now in looking at the table of these values, the y value (corresponding to height) is equal to zero at some point in time. Now if one were to look at the table of values, and see that the height is equal to zero feet at some point, is it true that this is not actually 0 ft, since we started from 3 feet? And if we wanted to find out when the ball hit the ground, we'd need to find when the ball was at -3 feet?

 

[fresh_42]

Suppose a baseball is hit 3 feet above the ground, and that it leaves the bat at a speed of 100 miles an hour at an angle of 20° from the horizontal.

I've got the parametric equations in terms of x and in terms of y, and I have values plotted and a graph sketched. My question is in regards to the initial height of 3 ft, and the position of the ball when it hits the ground. Now in looking at the table of these values, the y value (corresponding to height) is equal to zero at some point in time. Now if one were to look at the table of values, and see that the height is equal to zero feet at some point, is it true that this is not actually 0 ft, since we started from 3 feet? And if we wanted to find out when the ball hit the ground, we'd need to find when the ball was at -3 feet?

This all depends on where you selected the origin of the coordinate system (height, width). The resulting parabola is the same, but the equations are different. Theoretically you can also set the origin at 2 ft height and end up with -1 ft, or at even more strange places, e.g. on the score board. However, the feet or the bat of the batter is somehow a natural gauge.

 

[opus]

So in this attached image, you can see that we're starting from 3 ft above ground. So as soon as the batter hits the ball, the ball will go through a trajectory path. On it's way back down, it will eventually hit 3 feet above ground level. In terms of the table of values, this would be a height of 0. However, this is clearly not the ground as we started from 3 ft. So, by the table of values, y=-3 is equal to ground level?

 

[Mark44]

So in this attached image, you can see that we're starting from 3 ft above ground. So as soon as the batter hits the ball, the ball will go through a trajectory path. On it's way back down, it will eventually hit 3 feet above ground level. In terms of the table of values, this would be a height of 0. However, this is clearly not the ground as we started from 3 ft. So, by the table of values, y=-3 is equal to ground level?

Yes. If your horizontal axis (the x-axis) is 3' above ground level, then y = -3 is at ground level.

 

[opus]

Thank you both!