# Maths

This question is about the motion of a firework rocket.
A firework rocket is fired vertically upwards from the ground. It accelerates uniformly from rest
with an acceleration of 8.0 for 5.0 s after which time the fuel of the rocket has all been used. 2 ms−
(a) (i) Sketch below a graph to show how the velocity of the rocket changes with time from
the moment it leaves the ground until the moment that it returns to the ground. Mark
on your sketch the time at which the fuel has run out, the time at which the rocket 1
t 2t
reaches its maximum height and the time at which it reaches the ground. 3t
(Note that you are not expected to give any quantitative values of velocity and time and
air resistance can be ignored.)
(ii) Comment on the area(s) under the graph that you have drawn.
.....................................................................
.....................................................................
(This question continues on the following page)
– 14 – M00/430/H(2)
220-227
(Question B2 continued)
[2]
[2]
[3]
[2]
[2]
In the following calculations you may ignore any effects of air resistance and take the acceleration
due to gravity, g 10 m s . −2 =
(b) Calculate the
(i) speed of the rocket when the fuel runs out.
.....................................................................
.....................................................................
(ii) height that the rocket reaches when the fuel has just run out.
.....................................................................
.....................................................................
(iii) maximum height reached by the rocket.
.....................................................................
.....................................................................
.....................................................................
(iv) time it takes the rocket to reach its maximum height.
.....................................................................
.....................................................................
(v) time that it takes to fall from its maximum height to the ground.
.....................................................................
.....................................................................
(This question continues on the following page)
– 15 – M00/430/H(2)
220-227 Turn over
(Question B2 continued)
[4]
(c) (i) On the axes below sketch graphs to show how the gravitational potential energy and the
kinetic energy of the rocket varies as it moves from the ground to its maximum height.
(Note that this is only a sketch graph; you do not need to add any numerical values.)
[1]
(ii) State one assumption, other than ignoring air resistance, that you have made in
sketching the above graph.
.....................................................................
[2]
(d) The rocket plus fuel initially have a mass of 0.16 kg. If the initial mass of the fuel is 0.02 kg,
calculate the maximum kinetic energy of the rocket when all the fuel has been used.
.........................................................................
.........................................................................
(e) Calculate the power delivered to the rocket by the rocket fuel. [2]
.........................................................................
.........................................................................
[2]
(f) Describe two consequences on the motion of the rocket as a result of air resistance acting on
the rocket.
.........................................................................
.........................................................................
.........................................................................
.........................................................................

1. 👍 0
2. 👎 1
3. 👁 333
1. Sorry its physics

1. 👍 0
2. 👎 0
2. Surely you have some ideas on some of the parts.
It's all based on h(t) = h0 + v0t + at^2
KE = 1/2 mv^2

So, how far do you get?

1. 👍 0
2. 👎 0
👨‍🏫
oobleck
3. oops ... 1/2 at^2

1. 👍 0
2. 👎 0
👨‍🏫
oobleck

## Similar Questions

1. ### physics

A test rocket is fired straight up from rest. The net acceleration is 20 m/s2 upward and continues for 4.0 seconds, at which time the rocket engines cease firing. What maximum elevation does the rocket reach?

2. ### physics

A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 79.0 m/s at ground level. The engines then fire, and the rocket accelerates upward at 3.90 m/s2 until it reaches an altitude of

3. ### physics

A small weather rocket weighs 14.7 N. The rocket is carried up by a balloon. The rocket is released from the balloon and fired, and its engine exerts an upward force of 10.2 N on the rocket. What is the acceleration of the rocket?

4. ### intro to physics

a toy rocket moving vertically upward passes by a 2.2m- high window whose sill is 7.0m above the ground. the rocket takes 0.17s to travel the 2.2m height of the wondow part a): what was the launch speed of the rocket ? assume the

1. ### Physics

A rocket that weighs 7840 N on earth is fired. The force of propulsion is + 10 440N. Determine a) the mass of the rocket, b) the acceleration of the rocket, c) the velocity of the rocket at the end of 8.0 s.

2. ### Alg/Trig

If h= -16t^2 + 112t represents the height of a​ rocket, in​ feet, t seconds after it was​ fired, when will the rocket hit the​ ground? (Hint: The rocket is on the ground when h equals=​0).

3. ### Common Core Math II A-CR

A firework is launched into the air from ground level with an initial velocity of 128 ft/s. If acceleration due to gravity is –16 ft/s2, what is the maximum height reached by the firework?

4. ### physics

The engine of a toy rocket supplies an average acceleration of 38.0 m/s/s to the rocket for an interval of 0.80 s. A.)If the toy roocket is launched vertically, how high does it rise in this interval? B.) How fast is the rocket

1. ### physics

A 15.0-kg test rocket is fired vertically from Cape Canaveral. Its fuel gives it a kinetic energy of 1961 J by the time the rocket motor burns all the fuel. What additional height will the rocket rise? m - how do you organize

2. ### Physics

A rocket is fired at an angle from the top of a tower of height h0 = 68.6 m . Because of the design of the engines, its position coordinates are of the form x(t)=A+Bt2 and y(t)=C+Dt3, where A, B, C , and D are constants.

3. ### physic

A sounding rocket, launched vertically upward with an initial speed of 79.0 m/s, accelerates away from the launch pad at 5.70 m/s2. The rocket exhausts its fuel, and its engine shuts down at an altitude of 1.15 km, after which it

4. ### Calculus

A rocket is fired vertically into the air at the rate of 6 miles/min. An observer on the ground is located 4 miles from the launching pad. When the rocket is 3 miles high, how fast is the angle of elevation between the rocket and