A 200 kg weather rocket is launched is fired straight up. It starts at rest and

Question

A 200 kg weather rocket is launched is fired straight up. It starts at rest and accelerates upward at 30 m/s2 for 30 s and then runs out of fuel. It subsequently continues upward and drops to the ground after reaching a maximum height. Ignore any air resistance effect. To help you set up the problem, you can assign variables for the height, velocity and time at the launch point as y0, v0, t0, the point where it runs out of fuel as y1, v1, t3.

A. What is the velocity of the rocket when it runs out of the fuel?

B. What the height at which it runs out of fuel?

C. What is the rocket’s maximum height and when does it reach this height?

Explanation / Answer

a. v1= v0 + at =0 + 30 x 30 =900 m/s

b. h1= voxt+ 1/2 x a x t^2 = 0 + 1/2 x 30 x 30^2= 13500 m

c. distance travelled after it runs out of the fuel = h= v1^2/2g= 900^2/(2 x 9.8)= 41326.53 m

maximum height = 13500 + 41326.53 = 54826.53 m

time taken for travelling h = 900/9.8=91.83 s

maximum height it will reach = 91.83 +30= 121.83 s

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