A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 81.0 m/s at ground level. The engines then fire, and the rocket accelerates upward at 3.90 m/s2 until it reaches an altitude of 1040 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of −9.80 m/s2. (You will need to consider the motion while the engine is operating and the free-fall motion separately.)(a) For what time interval is the rocket in motion above the ground? (b) What is its maximum altitude? km(c) What is its velocity just before it hits the ground?

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Asked Sep 19, 2019
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A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 81.0 m/s at ground level. The engines then fire, and the rocket accelerates upward at 3.90 m/s2 until it reaches an altitude of 1040 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of −9.80 m/s2. (You will need to consider the motion while the engine is operating and the free-fall motion separately.)

(a) For what time interval is the rocket in motion above the ground?
 


(b) What is its maximum altitude?
 km

(c) What is its velocity just before it hits the ground?
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Expert Answer

Step 1

Consider the three different motions the engine is subjected to. First when it is fired and travels a distance of 1040 m, second when engines fails but due to velocity it reaches to some more height in the space, and third, when it falls directly to ground under the force due to gravity.

 

Let u1,v1,a1,s1, t1 be the constraints of the first motion, u2,v2,a2,s2, t2 be the constraints of the second motion, and u3,v3,a3,s3, t3 be the constraints of the third motion.

Write the given quantities of the question.

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и 381 m/s а, - 3.9 m/s? s 1040 m и, 3D1 =0 m/s из а, — а, 3 -9.8 m/s?

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Step 2

Write the third kinematic equation of motion for the first motion.

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(81 m/s)+2(3.9 m/s(1040 m) 6561 m2/s2 8112 m2/s2 =14673 m2/s2 =121.13 m/s

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Step 3

Write the first kinematic equation of...

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1,—и, + at, 1, — и, а (121.13 m/s)-(81 m/s) 3.9 m/s2 = 10.28 s

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