Question

Model rocket engines are rated by their thrust force and by the impulse they provide. You can use this information to determine the time interval at which the engines fire. Two rocket engines provide the same impulse. The first engine provides 6 N of thrust for 2 s; the second provides 4 N of thrust.

For how long does this second engine fire?

Answer 1

Answer: 3 seconds

Explanation:

Since they provide the same impulse,

Impulse= Ft

F1 = 6N

t1 = 2s

F2= 4N

t2= ?

F1= Force of first engine

t1= time elapsed by first engine

F2= force of second engine

t2= time elapsed by second engine

F1t1 = F2t2

6 × 2 = 4t2

t2= 12/4

t2 = 3 seconds

Answer 2

This second engine fires for 3 s

$\texttt{ }$

Further explanation

Acceleration is rate of change of velocity.

$\large {\boxed {a = \frac{v - u}{t} } }$

$\large {\boxed {d = \frac{v + u}{2}~t } }$

a = acceleration (m / s²)v = final velocity (m / s)

u = initial velocity (m / s)

t = time taken (s)

d = distance (m)

Let us now tackle the problem!

$\texttt{ }$

Given:

thrust of first engine = F₁ = 6 N

elapsed time of first engine = t₁ = 2 s

thrust of second engine = F₂ = 4 N

Asked:

elapsed time of second engine = t₂ = 2 s

Solution:

We will use Newton's Law of Motion to solve this problem as follows:

$\Sigma F = ma$

$\Sigma F = m \Delta v \div t$

$\Sigma F = I \div t$

$\boxed {I = \Sigma F \times t}$ → Impulse Formula

$\texttt{ }$

Two rocket engines provide the same impulse :

$I_1 = I_2$

$\Sigma F_1 \times t_1 = \Sigma F_2 \times t_2$

$6 \times 2 = 4 \times t_2$

$12 = 4 \times t_2$

$t_2 = 12 \div 4$

$\boxed {t_2 = 3 \texttt{ s}}$

$\texttt{ }$

Learn more

• Velocity of Runner : https://brainly.com/question/3813437

• Kinetic Energy : https://brainly.com/question/692781

• Acceleration : https://brainly.com/question/2283922

• The Speed of Car : https://brainly.com/question/568302
• Average Speed of Plane : https://brainly.com/question/12826372
• Impulse : https://brainly.com/question/12855855
• Gravity : https://brainly.com/question/1724648

$\texttt{ }$

Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics