Question content area top
Part 1
What is the velocity​ (in ft divided by s​) of a sandbag 1.75 s after it is released from a​ hot-air balloon that is stationary in the​ air?

To find the velocity of the sandbag 1.75 seconds after it is released, we can use the following physics concepts:

### Given:
- The balloon is stationary when the sandbag is released, so the initial velocity (\( v_0 \)) of the sandbag is 0.
- The only force acting on the sandbag is gravity, which accelerates it downwards at \( g = 32 \, \text{ft/s}^2 \).

### Formula:
The velocity of the sandbag at time \( t \) can be calculated using the equation:

\[
v(t) = v_0 + g \cdot t
\]

Since \( v_0 = 0 \) (because the sandbag is released from rest):

\[
v(t) = g \cdot t
\]

### Substituting the values:
\[
v(1.75) = 32 \, \text{ft/s}^2 \times 1.75 \, \text{s}
\]

\[
v(1.75) = 56 \, \text{ft/s}
\]

### Answer:
The velocity of the sandbag 1.75 seconds after it is released is \( 56 \, \text{ft/s} \) downward.

Would you like more details or have any questions?

---

Here are some related questions you might consider:
1. What is the position of the sandbag 1.75 seconds after release?
2. How would the velocity change if the balloon was moving upwards at a constant speed?
3. What would be the impact on velocity if air resistance was considered?
4. How long would it take for the sandbag to hit the ground if released from a certain height?
5. How would the velocity change if the sandbag was released from an accelerating balloon?

**Tip:** When dealing with free-fall problems, always check if the initial velocity is zero or non-zero to apply the correct equation.

Learn how to calculate the velocity of a sandbag 1.75 seconds after it is released from a stationary hot-air balloon using physics principles. This problem involves using the velocity formula in free fall due to gravity (g = 32 ft/s^2). Suitable for high school students studying kinematics and free fall problems.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation