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Calculus
Section 2.7
What is the set up for (d)?
Section 2.7
What is the set up for (d)?
if rock is thrown upward on the planet Mars with velocity of 10m/s, its height (in meters) after t seconds is given by H=10t-1.86t^2
a. velocity after one second
v(1)=lim(h->0 (H(1+h)-H(1))/h)
v(1)=lim(h->0 (10(1+h)-1.86(1+h)^2-(10(1)-1.86(1^2))/h).........simplify
v(1)=lim(h->0 (6.28-1.86h))
=6.28
so, the velocity is 6.28m/s
b. velocity at t=a
doing same way as fot t=1
you get lim(h->0 (10-3.72a-1.86h)
=10-3.72a
so, at t=a, the velocity is 10-3.72a m/s
c
rock will hit surface when H=0
0=10t-1.86t^2
0=t(10-1.86t)
=> t=0 or t=5.38
d.
using result from part (b)
v(a)=10-3.72a if a=5.38
v(5.38)=10-3.72*5.38
v(5.38)=10-20.0136
v(5.38)=-10.0136 ≈ -10.01
the rock hits the surface with a velocity of ≈ -10.01 m/s