A potato was launched in the air using a potato gun. The function for the situation was h(t)=-16t^2+100t+10, where t was the time in seconds and h(t) was the height in feet.

Question

A.) What was the maximum height of the potato?

B.) What was the lowest height of the potato?

C.) What was the lowest time that applies to the actual situation?

D.) What is the greatest time that applied to the actual situation

E.) Using your answers to parts a through d, what is the domain and range of the function, as they apply to this situation?

Answer 1

h(t) = -16t² + 100t + 10

(A)

Maximum height occurs at the vertex of the height-vs.-time parabola, which is at

t = -100 / [2(-16)] sec = ? sec

Evaluate h(t) at this value of t to get maximum height.

(B)

The lowest height will be ground level (h=0) since it falls to the ground eventually.

(C)

The lowest time is the moment of launch, which is t=0

(D)

The greatest time is when the potato reaches the ground, which you find by setting h(t)=0 and solving the quadratic equation for t. The quadratic formula will give a negative and a positive solution. The positive solution is the time to reach the ground.

(E)

The domain of time is from zero to the result from part (D). The range of h(t) is from h=0 to the result from part (A).