# Vectors in a tennis match

## Homework Statement

A player stands with his feet at the point O and serves the ball from a point Y at
a height of 2.4000m vertically above O. Assume that the ball then travels in a
straight line directly over the net at the midpoint A, which is at a height of
0.9144 m, before bouncing at the point X.

Determine the position vector of any point on the line Y A, and hence find
the position vector of the point X. Deduce that the ball cannot land in the

## Homework Equations

Excuse my lack of vector notation, i,j and k should be in bold :)

$$t=(1-s)p+sq$$

## The Attempt at a Solution

$$t=(1-s)(0i, 0j, 2.4k) + s(11.8872i, 4.1148j, 0.9144k)$$

$$t=11.8872si + 4.1148sj + (2.4 - 1.4856s)k$$

I know I have to rearrange somehow and find i and j when k = 0, but thats about it.

#### Attachments

• 13.6 KB Views: 506

Related Introductory Physics Homework Help News on Phys.org
Delphi51
Homework Helper

In t(1-s)p + sq what does each variable mean?

It seems to me it is useful to draw a side-view sketch showing the height of the ball (y) as it travels across the court. I think the slope of this line must be found to predict the distance the ball travels before hitting the floor.

Hi Delphi,

In the formula, s is in between 0 and 1, p is the starting point, and q is the finishing point. this i am told is the equation for a straight line vector, s=0 is the start and s=1 is the end. I assume be rearranging somehow, i can get i & j at any wanted value for k.

Delphi51
Homework Helper

Okay, makes sense now. Your vector
$$11.8872si + 4.1148sj + (2.4 - 1.4856s)k$$
represents the path of the ball when different values of s are used.
You need to find the value of s that makes the k component zero:
2.4 - 1.4856s = 0
for the point when it has height zero.
Then you can use that value of s in the i and j components to find the position on the floor where it hits.

Hi Delphi,

Thanks for the help, I was trying that approach but forgot to take the K out :)

Solved, thanks again!