Problema Solution
How long will it take for a ball dropped from the top of a 225- foot building to hit the ground? Round your answer to two decimal places?
Answer provided by our tutors
the equation for the height of the ball h depending on the time t is given by
h(t) = (-1/2)g*t^2 + v0*t + h0
where
g = 9.81 m/s^2 is a given constant (the acceleration due to gravity)
v0 = 0 m/s in the initial velocity
h0 = 225 ft = 225*0.3048 m the initial height
h(t) = (-1/2)g*t^2 + 225*0.3048
we need to find t and t>0 such that h(t) = 0 that is
(-1/2)g*t^2 + 225*0.3048 = 0
by solving we find and consider the positive roots
t = 3.74 sec
click here to see the step by step solution of the equation
it will take 3.74 seconds for the ball to hit the ground.