A hotair balloonist, rising vertically with a constant speed of 5.00 m/s, releases a sandbag at the instant the balloon is 40.0 m above the ground. (See the figure) After it is released, the = 5.00 m/s sandbag encounters no appreciable air drag.

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**Educational Web Page: Understanding Motion and Velocity**

---

**Scenario: Hot Air Balloonist and Sandbag Release**

A hot air balloonist, ascending vertically at a steady speed of \(5.00 \, \text{m/s}\), releases a sandbag when the balloon is precisely \(40.0 \, \text{m}\) above the ground.

The sandbag, upon release, experiences no significant air resistance. 

**Diagram Description:**

The figure illustrates a hot air balloon rising vertically with arrows indicating a velocity \(v = 5.00 \, \text{m/s}\). The basket of the balloon is positioned \(40.0 \, \text{m}\) above the ground at the time of the sandbag's release.

---

**Problem Solving:**

**Part A: Sandbag Height After 0.253 Seconds**

Compute the position (height above the ground) of the sandbag \(0.253 \, \text{s}\) after its release.

\( h = \_\_\_\_\_ \, \text{m} \)

**Part B: Sandbag Height After 1.06 Seconds**

Compute the position of the sandbag \(1.06 \, \text{s}\) after its release.

\( h = \_\_\_\_\_ \, \text{m} \)

**Part C: Velocity Component After 0.253 Seconds**

Compute the \(x\) component of the velocity of the sandbag at \(0.253 \, \text{s}\) after its release. 

Take \(+x\) to be upward.

\( \_\_\_\_\_ \)

---

This problem encourages students to apply concepts of motion, velocity, and gravitational effects on free-falling objects, enhancing their understanding of physics principles.
Transcribed Image Text:**Educational Web Page: Understanding Motion and Velocity** --- **Scenario: Hot Air Balloonist and Sandbag Release** A hot air balloonist, ascending vertically at a steady speed of \(5.00 \, \text{m/s}\), releases a sandbag when the balloon is precisely \(40.0 \, \text{m}\) above the ground. The sandbag, upon release, experiences no significant air resistance. **Diagram Description:** The figure illustrates a hot air balloon rising vertically with arrows indicating a velocity \(v = 5.00 \, \text{m/s}\). The basket of the balloon is positioned \(40.0 \, \text{m}\) above the ground at the time of the sandbag's release. --- **Problem Solving:** **Part A: Sandbag Height After 0.253 Seconds** Compute the position (height above the ground) of the sandbag \(0.253 \, \text{s}\) after its release. \( h = \_\_\_\_\_ \, \text{m} \) **Part B: Sandbag Height After 1.06 Seconds** Compute the position of the sandbag \(1.06 \, \text{s}\) after its release. \( h = \_\_\_\_\_ \, \text{m} \) **Part C: Velocity Component After 0.253 Seconds** Compute the \(x\) component of the velocity of the sandbag at \(0.253 \, \text{s}\) after its release. Take \(+x\) to be upward. \( \_\_\_\_\_ \) --- This problem encourages students to apply concepts of motion, velocity, and gravitational effects on free-falling objects, enhancing their understanding of physics principles.
### Part D

**Problem Statement:**

Compute the \( x \) component of the velocity of the sandbag at 1.06 s after its release.
Take \( +x \) to be upward.

**Answer Box:**

\[
v_x = \boxed{\hspace{3cm}} \, \text{m/s}
\]

---

### Part E

**Problem Statement:**

How many seconds after its release will the bag strike the ground?

**Answer Box:**

\[
t = \boxed{\hspace{3cm}} \, \text{s}
\]

---

### Part F

**Problem Statement:**

How fast is it moving as it strikes the ground?

**Answer Box:**

\[
v = \boxed{\hspace{3cm}} \, \text{m/s}
\]

---

### Part G

**Problem Statement:**

What is the greatest height above the ground that the sandbag reaches?

**Answer Box:**

\[
h_{\text{max}} = \boxed{\hspace{3cm}} \, \text{m}
\]

---

There are no graphs or diagrams included in the image.
Transcribed Image Text:### Part D **Problem Statement:** Compute the \( x \) component of the velocity of the sandbag at 1.06 s after its release. Take \( +x \) to be upward. **Answer Box:** \[ v_x = \boxed{\hspace{3cm}} \, \text{m/s} \] --- ### Part E **Problem Statement:** How many seconds after its release will the bag strike the ground? **Answer Box:** \[ t = \boxed{\hspace{3cm}} \, \text{s} \] --- ### Part F **Problem Statement:** How fast is it moving as it strikes the ground? **Answer Box:** \[ v = \boxed{\hspace{3cm}} \, \text{m/s} \] --- ### Part G **Problem Statement:** What is the greatest height above the ground that the sandbag reaches? **Answer Box:** \[ h_{\text{max}} = \boxed{\hspace{3cm}} \, \text{m} \] --- There are no graphs or diagrams included in the image.
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