Question

A child throws a penny upward out of a window and watches it fall to the ground. The function f(t) = -16t^2 + t + 10 represents the penny's distance in feet above the ground t seconds after the penny is thrown. Approximately how many seconds does it take the penny to hit the ground?

a) 2.55 seconds
b) 3.0 seconds
c) 4.5 seconds
d) 1.75 seconds

Answer 1

To find out when the penny hits the ground, we must set the quadratic function for its height above the ground to zero and solve for time. The correct time when the penny hits the ground, ignoring the negative solution, is approximately 1.75 seconds.

Step-by-step explanation:

The function f(t) = -16t^2 + t + 10 represents the penny's distance in feet above the ground at time t seconds after it has been thrown. To find out the time it takes for the penny to hit the ground, we have to find the value of t when f(t) equals zero because it represents the time when the penny is at ground level.

Setting the function to zero and solving the quadratic equation, -16t^2 + t + 10 = 0, we can apply the quadratic formula. The formula gives us two solutions, and we are interested in the positive one since time cannot be negative. Ignoring the negative solution, we find that the time it takes for the penny to hit the ground is approximately 1.75 seconds.

The correct answer is: d) 1.75 seconds.