A rocket accelerates at 25m/s^2 for 5s before it runs out of fuel and dies. What is the maximum height reached by the rocket?

Question

Physics question

Answer 1

This problem must be solved in two parts.   

 

For the first five seconds, the rocket accelerates at 25 m/s/s.   At the end of those five seconds lets determine the height and velocity of the rocket.   

 

d = 1/2 * a * t^{2 =}   0.5 * 25 * 25 = 312.5 meters.

v = at  = 5 * 25 = 125 m/sec

 

After five seconds, the rocket continues upward while being slowed by gravity until it reaches a peak at which the velocity is zero.

0 = 245 m/sec - 9.8 m/s/s * t    t = 125/9.8 sec = 12.8 sec

 The height of the rocket at the this point is    d = 312.5 + 125*t - 0.5 *(9.8) * t²

 

Substitute the value of t= 12.8 in the above equation to get the final answer.

 

Answer 2

The applicable formula is height = 1/2 acceleration x time ^ 2