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Chapter 6: Q. 45 (page 156)

a. A rocket of mass mis launched straight up with thrust F→thrust. Find an expression for the rocket’s speed at height hif air resistance is neglected.

b. The motor of a 350g model rocket generates9.5 N thrust. If air resistance can be neglected, what will be the rocket’s speed as it reaches a height of 85 m?

Short Answer

Expert verified

a). An expression for the rocket's speed at height hif the air is neglected localid="1649520749864" v=2Fthrust-mgmh

b). The speed of the rocket at height 85m is 54 m/s

Step by step solution

01

Part a). Step 1. Finding an expression

We can start solution with Newton's second law

ma=Fthrust-mga=Fthrust-mgm

Now, we can determine speed from an expression that includes acceleration and height

localid="1649520770861" v=2ahv=2·Fthrust-mgm·h

02

Part b) Step 1. Find the speed

Given that,m=0.35kgFthrust=9.5Nh=85mg=9.81m/s2

If we substitute values in the previous rocket's speed expression, we get

v=2×(9.5-0.35×9.81)0.35×85=54.28≃54m/sapprox.

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