https://file.aiquickdraw.com/mathbot/file/1727326313333tvnciznc.jpg

Let's solve the two problems from the image:

---

### 5. Sebuah roket diluncurkan hingga mencapai ketinggian maksimum 123 meter...

The rocket is launched vertically until it reaches a maximum height of 123 meters. The acceleration due to gravity \( g \) is given as \( 10 \, \text{m/s}^2 \).

We need to calculate:
- The initial velocity of the rocket
- The time it takes for the rocket to reach maximum height.

#### 1. Initial velocity:
We use the equation of motion:
\[
v^2 = u^2 - 2gh
\]
where:
- \( v = 0 \, \text{m/s} \) (velocity at maximum height),
- \( h = 123 \, \text{m} \),
- \( g = 10 \, \text{m/s}^2 \) (gravitational acceleration),
- \( u \) is the initial velocity we need to find.

Rearranging the formula to solve for \( u \):
\[
u = \sqrt{2gh}
\]
Substituting the known values:
\[
u = \sqrt{2 \times 10 \times 123} = \sqrt{2460} \, \text{m/s}
\]
Calculating:
\[
u \approx 49.6 \, \text{m/s}
\]
So, the initial velocity of the rocket is approximately \( 49.6 \, \text{m/s} \).

#### 2. Time to reach maximum height:
We use the formula:
\[
v = u - gt
\]
Since \( v = 0 \) at the maximum height, we can rearrange this to solve for time \( t \):
\[
t = \frac{u}{g} = \frac{49.6}{10} = 4.96 \, \text{seconds}
\]
Thus, the rocket takes approximately \( 4.96 \, \text{seconds} \) to reach its maximum height.

---

### 6. Sebuah benda dilempar vertikal dengan kecepatan awal 15 m/s...

An object is thrown vertically with an initial velocity of \( 15 \, \text{m/s} \), and it reaches a height of \( 30 \, \text{meters} \). We need to determine how long the object stays in the air. \( g = 10 \, \text{m/s}^2 \).

#### 1. Time to reach maximum height:
At maximum height, the final velocity is zero. We use the following equation:
\[
v = u - gt
\]
Rearranging to solve for \( t \):
\[
t = \frac{u}{g} = \frac{15}{10} = 1.5 \, \text{seconds}
\]
So, it takes \( 1.5 \, \text{seconds} \) to reach maximum height.

#### 2. Time to fall back to the ground:
The time to fall is the same as the time to rise, so the total time in the air is:
\[
t_{\text{total}} = 2 \times 1.5 = 3 \, \text{seconds}
\]
Thus, the object stays in the air for \( 3 \, \text{seconds} \).

---

Would you like any more details or explanations for these solutions?

Here are 5 related questions to consider:
1. How would the solution change if the acceleration due to gravity was different (e.g., 9.8 m/s²)?
2. What is the relationship between initial velocity and maximum height in these types of problems?
3. How can you calculate the total distance traveled by the rocket in problem 5?
4. How does air resistance affect the motion of objects in vertical launch problems?
5. How would the time of flight change in problem 6 if the initial velocity were doubled?

**Tip:** Always remember that the time to rise is equal to the time to fall when considering free fall under constant gravity without air resistance.

5. Sebuah roket diluncurkan hingga mencapai ketinggian maksimum 123 meter. Percepatan gravitasi di tempat peluncuran tersebut dianggap sebesar 10 m/s². Hitung kecepatan awal roket dan waktu yang diperlukan roket untuk mencapai ketinggian maksimum.
6. Sebuah benda dilempar vertikal ke atas dengan kecepatan awal 15 m/s. Jika benda tersebut mencapai ketinggian 30 meter dari posisi awalnya dan g = 10 m/s², tentukan lamanya benda tersebut di udara.

Solve problems on rocket launches and vertical motion with detailed solutions. Calculate the initial velocity of a rocket reaching 123 meters and the total time an object stays in the air when thrown with an initial velocity of 15 m/s.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation