A model rocket is launched straight upward with an initial speed of 58 m/s. It a

Question

A model rocket is launched straight upward with an initial speed of 58 m/s. It accelerates with a constant upward acceleration of 1.00 m/s^2 until its engines stop at an altitude of 170 m. What is the maximum height reached by the rocket? How long after liftoff does the rocket reach its maximum height? How long is the rocket in the air?
A model rocket is launched straight upward with an initial speed of 58 m/s. It accelerates with a constant upward acceleration of 1.00 m/s^2 until its engines stop at an altitude of 170 m. What is the maximum height reached by the rocket? How long after liftoff does the rocket reach its maximum height? How long is the rocket in the air?

Explanation / Answer

fto find how long it takes the rocket to get 170 high

y=Vot + 0.5at2

170=58 t + 0.5*1*t2

we get the equation:

0.5t2+58t-170=0

then solve for t using the quadratic equation

we get: 2.86 secs

now we can get the velocity at that point

v=vo +at

v=(58+1*2.86)

V =60.86m/s

now the rocket is under the influence of gravity so the acceleration is 9.8m/s^2 and we can get how high it goes from there

V2=vo2+2ay where v=0 because at the highest point it stops.

Therefore:

y=-vo2/2a=-(60.86)2/(2*-9.8)=189 m

therefore the maximum height is 189 +170 = 359 mm

-------------------------------

V=v0+at

0=60.86+(-9.8t) solve for t

t=60.86/9.8

t = 6.21

total time is = 6.21+ 2.86 = 9.07 secs

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