Robaffonadorkdh

2022-09-06

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 $h(t)=-16{t}^{2}+48t+448$

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

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

Collin Gilbert

Beginner2022-09-07Added 11 answers

$h(t)=-16{t}^{2}+48t+448.$

a) Find the height after 2 seconds

$h(2)=-16(2{)}^{2}+48(2)+448=480$

Height after 2 seconds : 480 feet

480 feet

b) Find the height after 4 seconds

$h(2)=-16(4{)}^{2}+48(4)+448=384$

Height after 4 seconds : 384 feet

384 feet

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

When the baseball strikes the ground, height is 0.

h(t) = 0

$-16{t}^{2}+48t+448=0\phantom{\rule{0ex}{0ex}}{t}^{2}-3t-28=0\phantom{\rule{0ex}{0ex}}(t-7)(t+4)=0\phantom{\rule{0ex}{0ex}}t=7\text{or}t=-4$

As t = -4 is not a reasonable value for time, it is rejected.

t = 7

Time taken for the baseball to strike the ground : 7 seconds

7 seconds

a) Find the height after 2 seconds

$h(2)=-16(2{)}^{2}+48(2)+448=480$

Height after 2 seconds : 480 feet

480 feet

b) Find the height after 4 seconds

$h(2)=-16(4{)}^{2}+48(4)+448=384$

Height after 4 seconds : 384 feet

384 feet

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

When the baseball strikes the ground, height is 0.

h(t) = 0

$-16{t}^{2}+48t+448=0\phantom{\rule{0ex}{0ex}}{t}^{2}-3t-28=0\phantom{\rule{0ex}{0ex}}(t-7)(t+4)=0\phantom{\rule{0ex}{0ex}}t=7\text{or}t=-4$

As t = -4 is not a reasonable value for time, it is rejected.

t = 7

Time taken for the baseball to strike the ground : 7 seconds

7 seconds

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