Question

during a softball game a batter hits a ball upward from an initial height of 3ft the height in feet of the softball is given by s(t)=-16t^2+80t+3 where t is time in seconds and t.0 which is closest to time when the softball will be 50 ft above the grpund

A 0.67 seconds or 5.04 seconds
B 2.50 seconds
C 0.83 seconds or 3.55 seconds
D5.04 seconds

Answer 1

To find the time when the softball will be 50 ft above the ground, we need to determine when the height of the softball, given by the equation s(t) = -16t^2 + 80t + 3, is equal to 50 ft.

Setting s(t) equal to 50 and solving for t:
50 = -16t^2 + 80t + 3

Rearranging the equation to form a quadratic equation:
-16t^2 + 80t - 47 = 0

Using the quadratic formula to solve for t:
t = (-b ± √(b^2 - 4ac)) / (2a)

where a = -16, b = 80, and c = -47:

t = (-80 ± √(80^2 - 4(-16)(-47))) / (2(-16))
t = (-80 ± √(6400 - 2992)) / (-32)
t = (-80 ± √3408) / (-32)
t = (-80 ± 58.37) / (-32)

Calculating both solutions:
t1 ≈ (-80 + 58.37) / (-32) ≈ 0.57 seconds
t2 ≈ (-80 - 58.37) / (-32) ≈ 5.42 seconds

Therefore, the closest time when the softball will be 50 ft above the ground is approximately 0.57 seconds. The correct option is not listed, so the closest option is C: 0.83 seconds or 3.55 seconds.