11. A rocket takes off vertically from the launch pad with no initial velocity b

Question

11. A rocket takes off vertically from the launch pad with no initial velocity but a constant up ward acceleration of 2.25 m/s2. At 15.4 s after blastoff, the engines fail completely so the only force on the rocket from then on is the pull of gravity. (8) What is the maximum height the rocket wil reach above the launch pad? (b) How fast is the rocket moving at the instant before it crashes onto the launch pad? (c) How long after engine failure does it take for the rocket to crash onto the launch pad?

Explanation / Answer

here,

when the rocket is accelrating

accelration , a = 2.25 m/s^2

time taken , t1 = 15.4 s

the height achived , h0 = 0 + 0.5 * a * t1^2

h0 = 0 + 0.5 * 2.25 * 15.4^2 m

h0 = 266.8 m

the final speed , u = 0 + a * t1

u = 0 + 2.25 * 15.4 m/s

u = 34.7 m/s

a)

the maximum height gained , h = h0 + u^2 /2g

h = 266.8 + 34.7^2 /( 2 * 9.81) m

h = 328 m

b)

the speed of rocket at the instant before it crashes onto the launch pad , v = sqrt(2*g*h)

v = sqrt(2*328 * 9.81) m/s

v = 80.2 m/s

c)

let the time taken be t2

h0 = - u * t2 + 0.5 * g * t2^2

266.8 = - 34.7 * t2 + 0.5 * 9.81 * t2^2

solving for t2

t2 = 11.7 s

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