Question

18 The exhaust gas of a rocket is expelled at the rate of 1300 kg/s, at the velocity of 50 000 m/s. Find the thrust on the rocket in newtons
6.5×107
3.5×107
7.6×107
5.7×107

19 A force of
2i⃗ +7j⃗
N acts on a body of mass 5kg for 10 seconds. The body was initially moving with constant velocity of
i⃗ −2j⃗
m/s. Find the final velocity of the body in m/s, in vector form.
5i⃗ +12j⃗
12i⃗ −5j⃗
10i⃗ −7j⃗
7i⃗ +10j⃗

Answer 1

Answer on Question #58110, Physics / Mechanics

18 The exhaust gas of a rocket is expelled at the rate of $1300\,\mathrm{kg/s}$, at the velocity of $50\,000\,\mathrm{m/s}$. Find the thrust on the rocket in newtons

$6.5 \times 10^{7}$

$3.5 \times 10^{7}$

$7.6 \times 10^{7}$

$5.7 \times 10^{7}$

Solution:

Newton’s second law of motion can be expressed as:

$$F = m a = m \frac{d v}{d t} = \frac{d p}{d t}$$

For the rocket:

$$\frac{d p}{d t} = v \frac{d m}{d t}$$

Hence:

$$F = v \frac{d m}{d t} = \left(50000 \frac{m}{s}\right) \cdot \left(1300 \frac{k g}{s}\right) = 6.5 \cdot 10^{7} N$$

Answer: $6.5 \cdot 10^{7} N$

19 A force of $2i^+ + 7j^+ N$ acts on a body of mass 5kg for 10 seconds. The body was initially moving with constant velocity of $i^+ - 2j^+ m/s$. Find the final velocity of the body in m/s, in vector form.

$$5i^+ + 12j^+$$ $$12i^+ - 5j^+$$ $$10i^+ - 7j^+$$ $$7i^+ + 10j^+$$

**Solution:**

Newton's second law of motion can be expressed in equation form as follows:

$$\vec{F} = m \vec{a}$$

where $m$ is mass of the body, $F$ is force, $a$ is acceleration.

The acceleration is

$$\vec{a} = \frac{\vec{F}}{m}$$

Velocity equals:

$$\vec{v} = \vec{v_0} + \vec{a}t$$

Substituting:

$$\vec{v} = \vec{i} - 2\vec{j} + \frac{2\vec{i} + 7\vec{j}}{5} \cdot 10 = \vec{i} - 2\vec{j} + 4\vec{i} + 14\vec{j} = 5\vec{i} + 12\vec{j}$$

Answer: $5\vec{i} + 12\vec{j}$

http://www.AssignmentExpert.com/