Question

What is the position vector, rtarget, that originates from the balloon's original position and terminates at the target? Put this in terms of h and d, and represent it as a vector using i and j?

Answer 1

The position vector is
`d\hat{i}-h\hat{j}`

Explanation :

Given that,

Height = h

Distance = d

Suppose, A student throws a water balloon with speed v₀ from a height h = 1.98 mat an angle θ = 21° above the horizontal toward a target on the pound. The target is located a horizontal distance d = 65 in from the student's feet. Assume that the balloon moves without air resistance. Use a Cartesian coordinate system with the origin at the balloon's initial position

We know that,

The initially position vector is

`s_(i)=0\hat{i}+h\hat{j}`

The final position vector is

`s_(f)=d\hat{i}+0\hat{j}`

We need to calculate the position vector

Using formula of position vector

`r=s_(f)-s_(i)`

Put the value into the formula

`r=d\hat{i}+0\hat{j}-0\hat{i}-h\hat{j}`

`r=d\hat{i}-h\hat{j}`

Hence, The position vector is
`d\hat{i}-h\hat{j}`