A ball is hurled in the air such that its horizontal (x) and vertical (y) shifts are given by the functions x (t) = 20t and y (t) = 40t - 5t2, where x and y are in meters and the time t is in seconds. What is the ratio of y to x at time t = 5 seconds?

0.25

0.50

0.75

0.85

x (t) = 20t

y (t) = 40t - 5t^2

Since we are only interested in comparing the two at time t = 5 seconds, we plug in 5 everywhere we see the variable t and then compare x and y

x (5) = 20 (5) becomes x (5) = 100

y (5) = 40 (5) - 5 (5) ^2 becomes y (5) = 200 - 125 and then y (5) = 75

The ratio of y to x can be expressed as: y/x, so we can say the ratio is equal to 75/100 or 0.75

Answer: 0.75