Rocket Vertical Acceleration: Calculating Time to Reach Maximum Point

Question:

A rocket is fired vertically up from the ground with a resultant vertical acceleration of 15 ms^-2.The fuel is finished in 1 minute and it continues to move up.What is the time taken for the rocket to reach its maximum point? (take g =10 ms^-2 )

Solution: Vertical acceleration- calculating time to reach maximum point

Total time taken for the rocket to reach its maximum point (T):

$${T =T_1+T_2}$$

T₁ – Time taken for the powered ascent (in second)

T2- Time taken for the free ascent, after the fuel is exhausted (in second)

To calculate T₁ (Time taken for powered ascent)

Velocity at the end of powered ascent

$${v_1=u+a_1 T_1}$$

v₁ – velocity at the end of powered ascent

u=0

a₁ =+15 ms^-2 (Resultant vertical acceleration of the rocket)

T₁ = 60 sec

$${v_1=0+(15)(60)}$$

$${v_1=900 \ \frac{m}{s}}$$

To calculate T2, after the fuel exhausted(Free ascent)

$${v=u+at}$$

$${0=900+(-10) T_2}$$

$${10T_2=900}$$

$${T_2=90 \ sec}$$

Total time taken for the rocket to reach its maximum point (T)= 60 sec+90 sec =150 sec.