Question

Suppose that an arrow was fired vertically upward from a crossbow at ground level and that it struck the ground 20 seconds later. If air resistance may be neglected, find the initial velocity of the bolt and the maxim altitude that it reached.

Answer 1

height = -4.9t^2 + vt+ c
but it said "groundlevel" ---> c=0

height = -4.9t^2 + vt
0 = -4.9(400) + 20v
20v = 1960
v = 98
So the initial velocity was 98 m/s

height = -4.9t^2 + 98t

d(height)/dt = -9.8t + 98
= 0 at maximum height
-9.8t + 98 = 0
t = 10 seconds

(We should have known that since the time to up and come down was 20 seconds)

at t=10
height = -4.9(100) + 10(98) = 490 m <-- max height