posted by lily on .
Madison is standing on the roof of a building that is 350 feet above the floor. She throws a ball straight up with a velocity of 20 feet per second. How long will the ball be in the air before it hits the ground?
first we observe that the motion of the ball is uniformly accelerated motion (because of acceleration due to gravity while it's in the air), thus we use this formula to find time:
h = ho + vo*t - (1/2)*g*t^2
ho = initial height
vo = initial velocity
t = time
g = acceleration due to gravity (9.8 m/s^2 = 32 ft/s^2)
making the ground as the reference or the origin (thus at this point, the height = h = 0), ho is thus equal to 350
0 = 350 + 20*t - 1/2*32*t^2
0 = 350 + 20t - 16t^2
since it's a quadratic equation, we either factor it or use quadratic formula,
t = [-b +- sqrt(b^2 - 4ac)]/(2a)
t = [-20 +- sqrt(20^2 - 4(-16)(350))]/(2(-16))
t = [-20 +- 150.997]/(-32)
t = -4.09
t = 5.34
since time is always positive, we get the positive root:
t = 5.34 s
hope this helps~ :)
It depends on many factors not said in the problem. How high does the ball go before it starts coming down, for example.
The problem is not solvable.
Ok. Someone else was smarter than I. I should have waited, I guess.