Afalling object travels a distance given by the formula d=5t + 16t^2 ft, where t is measured in seconds. how long will it take for the object to traveled 74 ft?

The time it will take for the object to traveled 74 ft is:

The formula which represents the distance traveled by a falling objectin time t is given by:

Now, we are asked to find the time t required by the object in order to travel the distance of 74 ft.

i.e. we are asked to find t when d=74 ft.

i.e.

Now, we know that any quadratic equation of the type:

is solved using the quadratic formula:

Here,

Hence, on putting these value in the formula we have:

Since, the time can't be negative.

Hence, we have: