Projectile motion formula: $$ h=-16 t^{2}+v t+h_{0} $$ $$ t= $$ time, in seconds, since the measuring tape was $$ \begin{array}{l} ext { The system has no real solutions. What does this } \ ext { indicate about the worker's arms and the } \ ext { measuring tape? }\end{array} $$ $$ h= $$ height, in feet, above the ground They will never be at the same height at the

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Projectile motion formula: $$ h=-16 t^{2}+v t+h_{0} $$ $$ t= $$ time, in seconds, since the measuring tape was $$ \begin{array}{l}	ext { The system has no real solutions. What does this } \ 	ext { indicate about the worker's arms and the } \ 	ext { measuring tape? }\end{array} $$ $$ h= $$ height, in feet, above the ground They will never be at the same height at the

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To analyze the situation described in the projectile motion formula $$ h = -16 t^{2} + vt + h_{0} $$, we need to understand what it means when the system has no real solutions.

1. **Understanding the Formula**:
   - $$ h $$ represents the height of the projectile above the ground.
   - $$ t $$ is the time in seconds.
   - $$ v $$ is the initial velocity of the projectile.
   - $$ h_{0} $$ is the initial height from which the projectile is launched.

2. **No Real Solutions**:
   - When we say that the system has no real solutions, it typically means that the quadratic equation derived from the projectile motion does not intersect the height $$ h $$ at any point in time $$ t $$.
   - This can occur if the discriminant of the quadratic equation is less than zero, indicating that the parabola does not touch the horizontal line representing the height.

3. **Interpretation**:
   - If the worker's arms and the measuring tape are represented by the height $$ h $$ and the projectile's motion, the fact that there are no real solutions indicates that the projectile (or the measuring tape) will never reach the height of the worker's arms.
   - This could imply that the initial height $$ h_{0} $$ is too low, or the initial velocity $$ v $$ is insufficient to reach the height of the worker's arms.

In summary, the absence of real solutions indicates that the projectile will never reach the height of the worker's arms, meaning they will never be at the same height.
The system having no real solutions means the projectile will never reach the worker's arms, so they will never be at the same height.

Projectile motion formula:

time, in seconds, since the measuring tape was
height, in feet, above the ground
They will never be at the same height at the

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