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
