Question

A vertical rocket has mass \(10,000\ \text{kg}\), thrust \(150,000\ \text{N}\) and drag \(20,000\ \text{N}\). The instantaneous acceleration (in \(\text{m/s}^2\)) is

• A. \(9.5\)
• B. \(2.8\)
• C. \(3.2\)
• D. \(4.0\)

Hint:

For a vertically ascending rocket, \[ \boxed{ a=\frac{T-D-mg}{m}. } \] Always subtract both the drag force and the weight from the thrust before dividing by the mass.

Answer 1

The Correct Option is C

Step 1: Write the forces acting on the rocket. For upward motion, \[ \boxed{ F_{\text{net}}=T-D-W, } \] where
• \(T\) = thrust,
• \(D\) = drag,
• \(W=mg\) = weight of the rocket.

Step 2: Substitute the given values. Given, \[ T=150000\ \text{N}, \] \[ D=20000\ \text{N}, \] \[ m=10000\ \text{kg}, \] \[ g=9.8\ \text{m/s}^2. \] Weight of the rocket is \[ W=10000\times9.8=98000\ \text{N}. \] Hence, \[ F_{\text{net}} = 150000-20000-98000 = 32000\ \text{N}. \]

Step 3: Calculate the acceleration. Using Newton's second law, \[ F_{\text{net}}=ma, \] \[ a=\frac{32000}{10000} =3.2\ \text{m/s}^2. \] Therefore, \[ \boxed{3.2\ \text{m/s}^2} \] is the correct answer. Thus, \[ \boxed{(C)} \] is the correct answer.