A2) A rocket is fired from rest at x = 0 and travels along a parabolic trajectory described by y² = {120(103)x} m. If the x component of acceleration is a, = (1/4t²) m/s²,where t is in seconds, determine the magnitude of the rocket's velocity and acceleration when t 10 s.

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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A2) A rocket is fired from rest at x = 0 and travels along a parabolie trajectory described by y? =
{120(10)x} m. If the x component of acceleration is a, = (1/4t?) m/s?,where t is in seconds,
determine the magnitude of the rocket's velocity and acceleration when t = 10 s.
y? = 120(103)x --- (1)
-(Gr) --- )
G-)
(221) –
a8 = )
ax = ï =
(2)
di
from (2): ax
dt
=) dt
t2
: di
= - =
.. i =
(at t = 0: x, = 0)
%3D
)---)
* Vz = i =
- - -
1
* Vx = i =
= dx
dt
(at t = 0:x, = 0)
12
48
P () -
Sub (4) into (1): y? = 120(10³)(t)
* y = 50t2
= ý = 100t
= ÿ = 100
At t = 10 s:
i = 83.33 m/s; ý = 1000 m/s;
= v = V83.332 + 10002 = 1003.5 m/s
* = 25 m/s?; ÿ = 100 m/s2: = a = v252 + 1002
103.5 m/s?
Transcribed Image Text:A2) A rocket is fired from rest at x = 0 and travels along a parabolie trajectory described by y? = {120(10)x} m. If the x component of acceleration is a, = (1/4t?) m/s?,where t is in seconds, determine the magnitude of the rocket's velocity and acceleration when t = 10 s. y? = 120(103)x --- (1) -(Gr) --- ) G-) (221) – a8 = ) ax = ï = (2) di from (2): ax dt =) dt t2 : di = - = .. i = (at t = 0: x, = 0) %3D )---) * Vz = i = - - - 1 * Vx = i = = dx dt (at t = 0:x, = 0) 12 48 P () - Sub (4) into (1): y? = 120(10³)(t) * y = 50t2 = ý = 100t = ÿ = 100 At t = 10 s: i = 83.33 m/s; ý = 1000 m/s; = v = V83.332 + 10002 = 1003.5 m/s * = 25 m/s?; ÿ = 100 m/s2: = a = v252 + 1002 103.5 m/s?
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