A test rocket starting from rest at point A is launched by accelerating it along

Question

A test rocket starting from rest at point A is launched by accelerating it along a 200.0-m incline at 1.40 m/s2 (Figure 1 ). The incline rises at 35.0r above the horizontal, and at the instant the rocket leaves it, its engines turn off and the rocket is subject to gravity only (ignore air resistance). Find the maximum height above the ground that the rocket reaches. Express your answer with the appropriate units. Find the rockets greatest horizontal range beyond point A. Express your answer with the appropriate units.

Explanation / Answer

a)

From

V2=Vo2+2ad

Speed of rocket as it leaves the incline is

Since it starts from rest Vo=0

=>V2=0+2*1.4*200

V=sqrt[560]=23.66 m/s

From

VY2=VoY2-2g(H-Y)

at maximum height VY=0

=>0 =(23.66sin35)2-2*9.81*(H-200Sin35)

H-200Sin35=9.4

H=124.1 m =124 m (approx)

b)

From

Y=Yo+Voyt-(1/2)gt2

=>0=(200sin35) +(23.66sin35)t -(1/2)*9.81*t2

4.905t2-13.573t-114.72=0

t=6.4137 s

Horizontal distance travelled

D=Xo+Voxt =200Cos35+(23.66Cos35)*6.4137

D=288.16 m =288 m(approx)

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