EQUATION WORD PROBLEM

Question

A baseball is projected upward from the top of a 448-ft-tall building with an initial velocity of 48 feet per second. The height, ℎ, of the baseball above the ground at any time, 𝑡, in seconds, is given by the equation ℎ(𝑡) = −16𝑡 2 + 48𝑡 + 448.

a) Find the height after 2 seconds

b) Find the height after 4 seconds

c) Find the time it takes for the baseball to strike the ground

Answer 1

The height after 2 seconds simply plug in the time in the equation given for the height.

ℎ(𝑡) = −16𝑡 2 + 48𝑡 + 448, h(2) = -16(2)² + 48(2) + 448 = 480 ft

The height after 4 seconds is:.

h(2) = -16(4)² + 48(4) + 448 = 384 ft

the time it takes to hit the ground is the time at a height of zero, then 0 = −16𝑡 2 + 48𝑡 + 448, solve the quadratic equation −16𝑡 2 + 48𝑡 + 448 = 0 divide all terms by 16 and you have the simplified equation

-t² + 3t +28 = 0 , multiply terms by -1, then it becomes the quadratic equation t² -3t -28 = 0

solve for t ,

Δ = b² -4ac = (-3)² -4(1)(-28) = 121

t = 3 ± √ 121 /2 , t = 7 , and t = -4 , now time cannot be negative then positive value is the correct time

t = 7.0 sec

Answer 2

For a and b, plug t=2 and t=4 into h(t) and solve.

For c, set h(t) equal to 0 and solve:

0=-16t²+48t+448

0=-16(t²-3t-28)

0=-16(t+4)(t-7)

Then t=-4 or t=7

So, it takes 7 seconds for the baseball to strike the ground

Answer 3

a) Put 2 in for t

h(2) = -16(2)²+48(2)+448 = 480 feet

b) Put 4 in for t

h(4) = -16(4)²+48(4)+448 = 384 feet

c) height of the ball when it hits the ground is 0, so put 0 in for h

0 = -16x² + 48x +448

I would suggest quadratic formula

x= -b ±√b²-4ac/2a

x = -48 + √(48²-4(-16)(448) = 128/(2*-16) = 4 doesn't make sense

x = -48 - √(48²-4(-16)(448) = -224/(2*-16) = 7

The baseball will hit the ground after 7 seconds