How long is a ball in flight

Question

A ball after being thrown straight up into the air with a velocity of 60 ft/sec, has a height t seconds after being thrown.  The flight of the ball can be represented by the equation: h=-15t^2 +150t (ignoring air resistence).  How long is the ball in flight?

Answer 1

The given equation is not correct.  The height as a function of time is

 

h(t) = -gt²/2 + v₀t + h₀

 

g = 32 ft/s²

v₀ = 60 ft/s  [given]

h₀ = 0  [if tossed from the ground]

 

h(t) = -16t² + 60t

 

The flight ends when the ball reaches the ground again, so set

 

h(t) = 0

 

and solve for t.

 

-16t² + 60t = 0

 

t(-16t + 60) = 0

 

The moment of tossing is

 

t = 0,

 

so the time in flight must be the solution to

 

-16t + 60 = 0

 

Solve this to get t in seconds, and finish from here.