Question

Siska hit a golf ball into the air with an initial velocity of 56 feet per second. The height h in feet of the ball above the ground can be modeled by h=-16t^{2}+56t, where t is the time in seconds after Sisika hit the ball. Find the time it takes the ball to reach 49 feet above the ground.

Answer 1

Answer: t=1.75secs

Explanation: The hieght h is related to the time by the given equation

h = -16t² + 56t

Swapping the equation left to right the sign changes

16t² - 56t =-h

But h = 49ft

16t² -56t = -49

Taking -49 to the other side of the equation and equating everything to 0 we have

16t² - 56t + 49 = 0

This is a quadratic equation

Where a=16 , b=-56 and c = 49

t = {- b +or- √{b² - 4*a*c} }/2*a

Substituting in the values correctly we would be left with

t = 56/2*a

= 56/32 =1.75sec

Answer 2

To find the time it takes for the ball to reach the given height, we need an equation that relates the height and time it travel which is given to be h=-16t^{2}+56t. We just substitute the height of 49 feet then solve for t. We do as follows:

h=-16t^{2}+56t
49 = -16t^{2}+56t
t = 1.75 seconds

Hope this answers the question. Have a nice day.