Jenna ate a shrinkroom that caused her to become one-hundredth of her original
size. At this size, Jenna is still able to jump with an initial speed of 2.20
m/s at an angle of 21.0 degrees with respect to the horizontal. If Jenna made
one of these such jumps, how far from her original position could she jump? assume gravity is 10m/s^2

To find how far Jenna could jump, we need to analyze the motion of her jump as a projectile. We will use the following projectile motion formulas:

### Key components:
1. **Initial speed** \( v_0 = 2.20 \, \text{m/s} \)
2. **Launch angle** \( \theta = 21.0^\circ \)
3. **Acceleration due to gravity** \( g = 10 \, \text{m/s}^2 \)

We will break her initial velocity into horizontal and vertical components:
- Horizontal velocity component:
  \[
  v_{0x} = v_0 \cos(\theta)
  \]
- Vertical velocity component:
  \[
  v_{0y} = v_0 \sin(\theta)
  \]

The time \( t \) Jenna spends in the air can be determined from the vertical motion. The total time of flight depends on when she returns to the ground (when her vertical displacement is zero). The vertical displacement equation is:
\[
y(t) = v_{0y} t - \frac{1}{2} g t^2
\]
Since \( y(t) = 0 \) when she lands, the time to land is given by:
\[
t_{\text{flight}} = \frac{2 v_{0y}}{g}
\]

Finally, we can find the horizontal range \( R \) (how far she jumps) using:
\[
R = v_{0x} \cdot t_{\text{flight}}
\]

### Step-by-step calculations:

1. **Horizontal and vertical velocity components**:
   \[
   v_{0x} = 2.20 \cos(21.0^\circ) \approx 2.20 \times 0.9336 = 2.054 \, \text{m/s}
   \]
   \[
   v_{0y} = 2.20 \sin(21.0^\circ) \approx 2.20 \times 0.3584 = 0.789 \, \text{m/s}
   \]

2. **Time of flight**:
   \[
   t_{\text{flight}} = \frac{2 v_{0y}}{g} = \frac{2 \times 0.789}{10} \approx 0.158 \, \text{seconds}
   \]

3. **Horizontal range**:
   \[
   R = v_{0x} \cdot t_{\text{flight}} = 2.054 \times 0.158 \approx 0.325 \, \text{meters}
   \]

Thus, Jenna could jump approximately **0.325 meters** (or 32.5 cm) from her original position.

Would you like more details on any of these steps or have any questions?

### Relative questions:
1. How does changing the launch angle affect the range of a projectile?
2. What would happen to the jump distance if Jenna’s initial speed were doubled?
3. How does the value of gravity impact projectile motion in general?
4. How do air resistance and other forces affect a real-world jump compared to an idealized scenario?
5. What would be the difference in the jump distance if Jenna's size didn't change?

**Tip**: Breaking down velocity into horizontal and vertical components is key when solving projectile motion problems.

Jenna ate a shrinkroom that caused her to become one-hundredth of her original size. At this size, Jenna is still able to jump with an initial speed of 2.20 m/s at an angle of 21.0 degrees with respect to the horizontal. If Jenna made one of these such jumps, how far from her original position could she jump? Assume gravity is 10 m/s^2.

Learn how to solve a projectile motion problem where Jenna, at one-hundredth of her original size, jumps with an initial speed of 2.20 m/s at a 21.0-degree angle. This solution involves breaking down the velocity into horizontal and vertical components, calculating the time of flight, and determining the horizontal range. Suitable for students in Grades 9-12.

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