Suppose that, when a stone is thrown upwards with a speed of 120 ft/sec, its height, h feet, after t seconds, is given by $h ( t ) = 120 t - 16 t ^ { 2 }$ The maximum height of the stone is

A)200 ft
B)225 ft
C)240 ft
D)250 ft
E)280 ft

Question

Suppose that, when a stone is thrown upwards with a speed of 120 ft/sec, its height, h feet, after t seconds, is given by $h ( t ) = 120 t - 16 t ^ { 2 }$ The maximum height of the stone is

A)200 ft
B)225 ft
C)240 ft
D)250 ft
E)280 ft

Quizplus · Accepted Answer

The maximum height of the stone can be found by completing the square or using the vertex formula for a parabola. The equation given is in the form $h(t) = -16t^2 + 120t$. The vertex of this parabola, which gives the maximum height, occurs at $t = -\frac{b}{2a}$, where $a = -16$ and $b = 120$. Thus, $t = -\frac{120}{2(-16)} = \frac{120}{32} = 3.75$ seconds. Plugging this back into the equation for $h(t)$ gives the maximum height: $h(3.75) = 120(3.75) - 16(3.75)^2 = 450 - 225 = 225$ ft.

Suppose That, When a Stone Is Thrown Upwards with a Speed