Give step-by-step solution with explanation and final answer:
A
7
0
.
0
kg skydiver leaps out of an airplane.
2
.
0
0
seconds later, a
2
9
.
0
N drag force is acting on them. They continue ac

Question

Give step-by-step solution with explanation and final answer:
A 
7
0
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0
 ﻿kg skydiver leaps out of an airplane. 
2
.
0
0
 ﻿seconds later, a 
2
9
.
0
 ﻿N drag force is acting on them. They continue accelerating downwards, with their increasing speed causing a larger and larger drag force until, 
1
0
.
0
 ﻿seconds after they leapt, they reach terminal velocity. After that point, they fall with a constant speed. a
)
 ﻿What is the skydiver
’
s acceleration 
2
.
0
0
 ﻿seconds after they leapt? 
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 ﻿b
)
 ﻿What is the net force on the skydiver 
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0
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 ﻿seconds after they leapt? 
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VIPSolutions · Accepted Answer

# Skydiver Free Fall with Air Resistance

## Given Data

- Mass of skydiver, $ m = 70.\,\mathrm{kg} $
- Gravitational acceleration, $ g = 9.8\,\mathrm{m/s^2} $
- Drag force at $ t = 2.00\,\mathrm{s} $, $ F_{\mathrm{drag}} = 29.\,\mathrm{N} $
- Skydiver reaches terminal velocity at $ t = 10.\,\mathrm{s} $

---

## a) Acceleration at $ t = 2.00\,\mathrm{s} $

### Step 1: Find the Gravitational Force

$$
F_g = mg = 70. \times 9.8 = 686\,\mathrm{N}
$$

### Step 2: Net Force at $ t = 2.00\,\mathrm{s} $

$$
F_{\text{net}} = F_g - F_{\mathrm{drag}} = 686 - 29. = 657\,\mathrm{N}
$$

### Step 3: Use Newton’s Second Law to Find Acceleration

$$
a = \frac{F_{\text{net}}}{m} = \frac{657}{70.} = 9.39\,\mathrm{m/s^2}
$$

---

**Final Answer (a):**

$$
\boxed{9.39\,\mathrm{m/s^2}}
$$

The skydiver's acceleration $2.00\,\mathrm{s}$ after leaping is **9.39 m/s² downward**.

---

## b) Net Force at $ t = 10.\,\mathrm{s} $ (Terminal Velocity)

### Step 1: At Terminal Velocity

- The forces are balanced: $ F_g = F_{\mathrm{drag}} $
- Net force is zero because speed is constant.

### Step 2: State the Net Force

$$
F_{\text{net}} = \,\mathrm{N}
$$

---

**Final Answer (b):**

$$
\boxed{\,\mathrm{N}}
$$

The net force on the skydiver $10.\,\mathrm{s}$ after leaping is ** N**.

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