Question

In: Math

A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds...

A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is given by a(t) = 60t ft/s2 , at which time the fuel is exhausted and it becomes a freely “falling” body and falls to the ground.

(a) Determine the position function s(t) for all times t > 0.

(b) What is the maximum height achieved by the rocket? (

c) At what value of t does the rocket land?

Solutions

Expert Solution

comment if you need further clarification!

milcah answered 2 years ago
Next > < Previous

Related Solutions

A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds...
A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t)=96t, at which time the fuel is exhausted and it becomes a freely "falling" body. 1919 seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to −16 ft/s in 5 s. The rocket then "floats" to the ground at that rate. (a) Determine the position function s and the velocity function v(for all times t). v(t)=    if 0≤t≤3    ...
A rocket is fired straight upward, starting from rest with an acceleration of 25.0 m/s2. It...
A rocket is fired straight upward, starting from rest with an acceleration of 25.0 m/s2. It runs out of fuel at the end of 4.00 s and continues to coast upward, reaching a maximum height before falling back to Earth. (a) Find the rocket’s height when it runs out of fuel; (b) find the rocket’s velocity when it runs out of fuel; (c) find the maximum height the rocket reaches; (d) find the rocket’s velocity the instant before the rocket...
2. A rocket is fired vertically with an upward acceleration of 20 m/s2. After 25 s,...
2. A rocket is fired vertically with an upward acceleration of 20 m/s2. After 25 s, the engine shuts off and the rocket continues as a free particle. (a) Find the highest point the rocket reaches. (b) Find the total time the rocket is in the air. (c) Draw the graph acceleration versus time for the motion. d) Draw the graph velocity versus time for the motion. (e) Draw the graph position versus time for the motion. (f) On each...
a toy rocket is fired fired at rest vertically upwards and accelerates at a constant rate....
a toy rocket is fired fired at rest vertically upwards and accelerates at a constant rate. At the instant the engine cuts out, the rocket has risen to 52 m and acquired a velocity of 80 m/s. The rocket continues to rise in unpowered flight, reaches maximum height, and falls back to the ground with negligible air resistance. The speed of the rocket upon impact on the ground is closest to
A rocket is fired vertically upward. At the instant it reaches an altitude of 1450 m...
A rocket is fired vertically upward. At the instant it reaches an altitude of 1450 m and a speed of 265 m/s, it explodes into three equal fragments. One fragment continues to move upward with a speed of 292 m/s following the explosion. The second fragment has a speed of 396 m/s and is moving east right after the explosion. What is the magnitude of the velocity of the third fragment? Answer in units of m/s
A 7400 kg rocket blasts off vertically from the launch pad with a constant upward acceleration...
A 7400 kg rocket blasts off vertically from the launch pad with a constant upward acceleration of 2.15 m/s2 and feels no appreciable air resistance. When it has reached a height of 550 m , its engines suddenly fail so that the only force acting on it is now gravity. a)What is the maximum height this rocket will reach above the launch pad? b)How much time after engine failure will elapse before the rocket comes crashing down to the launch...
A 7800 kg rocket blasts off vertically from the launch pad with a constant upward acceleration...
A 7800 kg rocket blasts off vertically from the launch pad with a constant upward acceleration of 2.15 m/s2 and feels no appreciable air resistance. When it has reached a height of 575 m , its engines suddenly fail so that the only force acting on it is now gravity. A) What is the maximum height this rocket will reach above the launch pad? b)How much time after engine failure will elapse before the rocket comes crashing down to the...
A 7450 kg rocket blasts off vertically from the launch pad with a constant upward acceleration...
A 7450 kg rocket blasts off vertically from the launch pad with a constant upward acceleration of 2.25 m/s2 and feels no appreciable air resistance. When it has reached a height of 500 m , its engines suddenly fail so that the only force acting on it is now gravity. A. What is the maximum height this rocket will reach above the launch pad? B. How much time after engine failure will elapse before the rocket comes crashing down to...
A rocket, initially at rest on the ground, accelerates upward with a constant acceleration of 94.0...
A rocket, initially at rest on the ground, accelerates upward with a constant acceleration of 94.0 m/s2 until it reaches a speed of 1.50×102 m/s when the engines are cut off. After that the rocket is in free-fall. What is the maximum height reached by the rocket ? What total time elapses between take-off and the rocket hitting the ground?
a rocket rises vertically from rest, with an acceleration of 3.2 m/s(s) until it runs out...
a rocket rises vertically from rest, with an acceleration of 3.2 m/s(s) until it runs out of fuel at an altitude of 845 m. After this point, its acceleration is that of gravity, downward. what is the velocity when the rocket runs out of fuel? how long does it take to reach that point? what is the maximum altitude and how long to reach it? what is the velocity when it strikes earth? how long is the rocket in the...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT