A rocket is launched straight up. It contains two stages (Stage 1 and Stage 2) o

Question

A rocket is launched straight up. It contains two stages (Stage 1 and Stage 2) of solid rocket fuel that are designed to burn for 10.0 and 5.0 s, respectively, with no time interval between them. In Stage 1, the rocket fuel provides a net upward acceleration of 18 m/s^2. In Stage 2, the net upward acceleration is 10 m/s^2. Neglecting air resistance, calculate the maximum altitude above the surface of Earth of the payload and the time required for it to return back to the surface. maximum altitude m time required s

Explanation / Answer

during stage 1:

a = 18 m/s^2

t = 10 sec

vf = vi + at = 0 + (18 x 10) = 180 m/s

d = vi t + a t^2 /2

d1 = 0 + (18)(10^2) / 2 = 900 m

During stage 2:

a = 10 m/s^2

t = 5 sec

vf = 180 + (10 x 5) = 230 m/s

d2 = (180 x 5) + (10 x 5^2 / 2)

d2 = 1025 m

after that it will be in free fall,

a = - 9.8 m/s^2

at maximum height, v= 0

vf^2 - vi^2 = 2 a d

0^2 - 230^2 = 2(-9.8)(d3)

d3 = 2700 m

Maximum height = d1+ d2 + d3 = 4624 m .........Ans

after stage 2:

v = +230 m/s

a = - 9.8 m/s^2

y = d1 +d2 = 1925 m

0 - 1925 = 230t - 9.8 t^2 /2

4.9 t^2 - 230t - 1925 = 0

t = 54.2 sec

total time = 10 + 5 + 54.2 = 69.2 sec ........Ans

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