Question

1.  A rocket is launched vertically from the Earth, and the thrust (pushing force) from the engines is directed upward, and has a magnitude of 5.00 x 10⁶ N. The mass of the rocket is initially 2.00 x 10⁵ kg.

(a)   What is the initial acceleration of the rocket, assuming you can neglect air resistance?

(b)   After the rocket has been in flight for a while, burning and exhausting a lot of fuel, its mass has decreased to 1.20 x 10⁵ kg, and its acceleration at this point is 25.0 m/s². What is the magnitude of the drag force (that is, the resistance from the air) at this point? Note that at this point the rocket's altitude is still low, so you can still take gravity to be g = 9.81 m/s².

2.  A falling body on Earth will generally not fall at constant acceleration in reality, due to air resistance (or drag). The equation for the drag force F_d is

F_d = 0.5 (C_d A) ρ v²

where C_d is the unitless drag coefficient of a body, A is its cross-sectional area, ρ is the density of the air, and v is the body's velocity with respect to the atmosphere.

(a) Look up typical values of C_d and A for a falling adult human being (without a parachute), and also the correct value of ρ, the atmospheric density near sea level on Earth. Then calculate the drag force on a person falling at a speed of 30.0 m/s through the atmosphere.

(b) Look up and then see if you can also calculate the terminal velocity (that is, the final nearly constant speed) that a falling, parachuteless person would have after diving from, let's say, a few kilometers up.

Answer 1

1) a) For the given mass m and force F, by Newton's 2nd law, acceleration is given by

b) We know for a rocket,