Question

If an object is projected upward from ground level with an initial velocity of 128 ft per sec, then it's height in feet after t seconds is given by s(t)=-16t^2+128t. Find the number of seconds it will take to reach its maximum height. What is this maximum height ?

Answer 1

Answer: t= 4 seconds

Maximum height = 256 feet

Step-by-step explanation:

The height of the object projected upwards after t seconds is given by

s(t)=-16t^2+128t.

The expression is a quadratic equation. When this equation is plotted on a graph, height against time, it takes the shape of a parabola whose vertex represents the maximum height attained by the object.

To get the value of t at the maximum height,

t = -b/2a

From the equation,

a = -16

b = 128

t = -128/-2×-16

= -128 /- 32= 4

it will take 4 seconds to reach its maximum height

To find maximum height attained, put t= 4 in the equation

s(t)=-16t^2+128t

S = -16× 4^2 + 128×4

S = -256+512

S = 256 feet