Problem 4: A catapult launches a test rocket vertically upwards from a well, giving the rocket an initial speed of 80 m/sec at ground level. The engines then fire, and the rocket accelerates upward at 4 m/sec² until it reaches an altitude of 1000 m. a) How long does it take the rocket to reach the altitude of 1000 m? Answer: 10 sec b) What is the speed of the rocket when it reaches an altitude of 1000 m? Answer: 120 m/sec Time t y 1000 m. t=0 Yo=0- Vo = 80 m/sec a = 4 m/sec² Engines On Vo ¯†à v = 0 m/sec When the rocket reaches an altitude of 1000 m, the engines fail and the rocket goes into free fall, with an acceleration of a = -g. For the remainder of this problem, the rocket engines will be off. We will re-define t = 0 sec to be the time when the rocket is at an altitude of 1000 m. The initial properties of the rocket will be the properties of the rocket at 1000. c) What is the largest height the rocket reaches? Answer: 1734.7 m d) What is the time it takes the rocket to hit the ground? Answer: 31.06 sec e) What is the velocity of the rocket just before it hits the ground? Answer: -184.4 m/sec AY Engines Off

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x = xót vót tật, ở = To +ất, v = vỏ +2āA,t=i
+
-b+√b²-4ac
2a
Transcribed Image Text:x = xót vót tật, ở = To +ất, v = vỏ +2āA,t=i + -b+√b²-4ac 2a
Problem 4:
A catapult launches a test rocket vertically upwards from a well, giving the rocket an initial
speed of 80 m/sec at ground level. The engines then fire, and the rocket accelerates upward at
4 m/sec² until it reaches an altitude of 1000 m.
a) How long does it take the rocket to reach the altitude of 1000 m? Answer: 10 sec
b) What is the speed of the rocket when it reaches an altitude of 1000 m? Answer: 120
m/sec
AY
Time t
y = 1000 m-
t=0
Yo
0.
Vo = 80 m/sec
a = 4 m/sec²
18
When the rocket reaches an altitude of 1000 m, the engines fail and the rocket goes into free
fall, with an acceleration of a = -g. For the remainder of this problem, the rocket engines will
be off. We will re-define t = 0 sec to be the time when the rocket is at an altitude of 1000 m.
The initial properties of the rocket will be the properties of the rocket at 1000.
v = 0 m/sec
Ymax
Engines On
c) What is the largest height the rocket reaches? Answer: 1734.7 m
d) What is the time it takes the rocket to hit the ground? Answer: 31.06 sec
e) What is the velocity of the rocket just before it hits the ground? Answer: -184.4 m/sec
AY
Redefine as t = 0
Yo = 1000 m
Vo = 120 m/sec
d=-g
g = 9.8 m/sec²
Engines Off
Įä
Transcribed Image Text:Problem 4: A catapult launches a test rocket vertically upwards from a well, giving the rocket an initial speed of 80 m/sec at ground level. The engines then fire, and the rocket accelerates upward at 4 m/sec² until it reaches an altitude of 1000 m. a) How long does it take the rocket to reach the altitude of 1000 m? Answer: 10 sec b) What is the speed of the rocket when it reaches an altitude of 1000 m? Answer: 120 m/sec AY Time t y = 1000 m- t=0 Yo 0. Vo = 80 m/sec a = 4 m/sec² 18 When the rocket reaches an altitude of 1000 m, the engines fail and the rocket goes into free fall, with an acceleration of a = -g. For the remainder of this problem, the rocket engines will be off. We will re-define t = 0 sec to be the time when the rocket is at an altitude of 1000 m. The initial properties of the rocket will be the properties of the rocket at 1000. v = 0 m/sec Ymax Engines On c) What is the largest height the rocket reaches? Answer: 1734.7 m d) What is the time it takes the rocket to hit the ground? Answer: 31.06 sec e) What is the velocity of the rocket just before it hits the ground? Answer: -184.4 m/sec AY Redefine as t = 0 Yo = 1000 m Vo = 120 m/sec d=-g g = 9.8 m/sec² Engines Off Įä
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