A rocket is propelled upward with an initial speed of 120 ft/sec. How high will the rocket go ?

Question

A rocket is propelled upward eith an initial speed  of 120 ft/sec. How high will the rocket go? How long will the rocket take to land? At what time will the rocket be at 100 ft of height ?

Answer 1

Hi Lina,

v = 0 (at the highest point , v₀ = 120 ft/sec, h = ? t_r = ? t₁₀₀ = ? g = 32.17 ft/sec²

v² = v₀² -2gh 

0² =(120ft/sec)² - 2(32.17ft/sec²)h

64.34h = 14400

         h = 14400/64.34 ft   [check with your calculator]

The height reached by the rocket is 224 feet

The equation of the distance traveled is

y= v_0yt- 1/2gt²

y = 0 when the rocket is just propelled from the ground and when it returns to the ground

0 = 120t - 1/2*32t²

0 = 120t -16 t²

0 = (120 -16t)t

 0 = t and

0 = 120-16t , t = 120/16 = 7.5

The rocket will return in 7.5 seconds

 if y = 100

y = v_oyt - 1/2gt²

100 = 120t -16t²

  25 = 30t -4t²

4t²-30t +25 = 0

Use the quadratic equation

a = 4, b = -30, c = 25

t = [30 ±√((-30)² - 4(4)(25))]/2(4)

t = [30±√(900-400)]/8

t = [30±√500]/8

t =[30±22.36]/8

t =[3.75±2.795]

t = 6.7 or 0.955

The rocket was at 100 feet 0.955 second after being propelled upward and again 100 feet at 6.7 seconds on the return trip.