Suppose that, when a stone is thrown upwards with a speed of 60 miles an hour, its height, h feet, after t seconds, is given by $h ( t ) = 88 t - 16 t ^ { 2 }$ The maximum height of the stone is

A)100 ft
B)120 ft
C)121 ft
D)125 ft
E)200 ft

Question

Suppose that, when a stone is thrown upwards with a speed of 60 miles an hour, its height, h feet, after t seconds, is given by $h ( t ) = 88 t - 16 t ^ { 2 }$ The maximum height of the stone is

A)100 ft
B)120 ft
C)121 ft
D)125 ft
E)200 ft

Quizplus · Accepted Answer

The maximum height of the stone can be found by determining the vertex of the parabola represented by the equation $h(t) = 88t - 16t^2$. The vertex form of a parabola is given by $-\frac{b}{2a}$ for the t-coordinate of the vertex, where $a = -16$ and $b = 88$ in this equation. Plugging these values into the formula gives the time at which the maximum height is reached: $-\frac{88}{2(-16)} = \frac{88}{32} = 2.75$ seconds. Substituting $t = 2.75$ back into the equation for $h(t)$ gives the maximum height: $h(2.75) = 88(2.75) - 16(2.75)^2 = 242 - 121 = 121$ feet.

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