Answer:
max height = 473.68 m
velocity hit mars = 60 m/s
Explanation:
Maximum height can be found by finding the 1st derivative of s(t) and equate it to zero.
s'(t) = ds/dt = 60 - 3.8t
s't() = 0
60 - 3.8t = 0
3.8t = 60
t = 60/3.8 = 15.79
subs t = 15.79 to s(t)
s(15.79) = 60(15.79) - 1.9(15.79)^2 = 473.68 m
b) The arrow will hit mars after it went up to the maximum height and travelled back downward due to gravity
Assuming the gravity constant, the velocity when it hit the ground should be the same as it leaves the ground. To confirm that, we tested with the equation of motion.
Since there is no gravity given, let a downward as g
v^2 = u^2 + 2as
The arrow shot upward will comes back downward. Since gravity is always constant, the time it took back to reach the ground should be the same as it goes up to max height
so, t = 2*15.79 = 31.58 s
s = 0 since we are looking at the moment it touches back the ground
v^2 = u^2 +2as
v^2 = 60^2 + 2g(0)
v^2 = 60^2
v = 60 m/s
