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An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at +15.0 m/s2. At t1 the rocket engine is shut down and the sled moves with constant velocity v until t2. The total distance traveled by the sled is 5.30 103 m and the total time is 89.0 s.
Find tl.
_____s
Find t2.
_____s
Find v.
_____m/s
--------NEXT question-------
A parachutist descending at a speed of 10.0 m/s loses a shoe at an altitude of 50.0 m. (Assume the positive direction is upward.)
(a) When does the shoe reach the ground?
______s
(b) What is the velocity of the shoe just before it hits the ground?
______ m/s

2007-05-24 14:28:46 · 1 answers · asked by Johnson 2 in Science & Mathematics Physics

1 answers

Problem one is a classic piecewise linear dynamic question.
From t0 to t1, the sled follows the equation (assuming constant mass)

s(t)=s0+v0*t+.5*a*t^2
and
v(t)=v0+a*t^2
for this time interval
s0=0, v0=0

s(t1)=.5*15*t1^2
=7.5*t1^2
and
v(t1)=15*t1

for the second time interval, the sled follows the same equations, but a=0, v0=v(t1) and s0=s(t1) and the actual time from start will be t+t1

the data given translates to
5,300=7.5*t1^2+15*t1*(89-t1)
or
0=7.5*t1^2-1335*t1+5300

This produces two roots, t1=4.1, and t1=174.
Since 174 is outside the range of t, we will use 4.1

The second interval is
t2=89-t1=89-4.1=84.9

check by substituting into the equations.

For the shoe drop, I will ignore air friction and use
50=10*t+9.81*t^2

the positive root is 1.8 s

v=10+9.81*1.8
27.685 m/s

j

2007-05-25 05:54:05 · answer #1 · answered by odu83 7 · 0 1

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