Question

A potato gun is a device made out of plastic pipe that launches a potato using compressed air. They can be great fun, and even educational for physics and math. A potato launched by a particular potato gun has a height described by h(t) = -16t² + 116t + 5. When is the potato 125 feet in the air? The potato is 125 feet in the air after ______ seconds on the way up and after ______ seconds on the way back down.

Answer 1

To find out when the potato is 125 feet in the air, we set the height function equal to 125 and solve for t. The potato is 125 feet in the air after approximately 1.18 seconds on the way up and approximately 6.82 seconds on the way back down.

Step-by-step explanation:

To find out when the potato is 125 feet in the air, we need to set the height function h(t) equal to 125 and solve for t. The height function is given as h(t) = -16t² + 116t + 5.

So, we have -16t² + 116t + 5 = 125.

Simplifying the equation, we get -16t² + 116t - 120 = 0.

Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. After solving, we find that the potato is 125 feet in the air after approximately 1.18 seconds on the way up and approximately 6.82 seconds on the way back down.