Physics help?

Question

A ball thrown vertically upward is caught by the thrower after 9.1 s.
(a) Find the initial velocity of the ball.
m/s (upward)
(b) Find the maximum height it reaches.
m

Can you show me how you get the answer because i dont know how you calculate displacement when a ball is thrown upward.

Answer 1

If we ignore air resistance, the equations are
y(t)=v0*t-.5*g*t^2
and
v(t)=v0-g*t

since we know the total flight time, when the ball returns to y=0
0=v0*9.1-.5*g*9.1^2
solve for v0

the max height is reached when v(t)=0
using v0 from above
0=v0-g*t
t=v0/g

plug this into y(t) to find the height
y(v0/g)=v0^2/g-.5*v0^2/g
or
y=.5*v0^2/g

j