PreCalculus
posted by Becky .
A pomegranate is thrown from a ground level straight up into the air at time t = 0 with velocity 67 feet per second. Its height at time t seconds is f(t)=16^2+67t.
(a) Find the time it hits the ground and (b) the time it reaches its highest point. (c) What is the maximum height?
Please round to two decimal places.

a) when it hits the ground, f(t) = 0
0 = 16t^2 + 67t
16t^2  67t = 0
t(16t  67) = 0
t = 0 or t = 67/16 = appr 4.19 seconds
t=0 would be the start of the toss
so the answer you want is t = 4.19 sec
b) since you labeled it "precalculus" I assume you cannot at this point take the derivative, too bad
so we have to complete the square
f(t) = 16t^2 + 67t
= 16(t^2  (67/16)t + 4489/1024  4489/1024)
= 16( (t  67/32)^2  4489/1024)
= 16(t  67/32)^2 + 4489/64
it will reach the maximum height at 67/32 or appr 2.09 sec, and that max height is 4489/64 or 70.14 ft
Notice we could have used the properties of the parabola to shorten this up a bit
since the xintercepts are 0 and 4.19, the vertex must lie midway between them
This would be 2.09 , the answer I got when completing the square. Subbing 2.09 in for f(2.09) gives us
16(2.09)^2 + 67(2.09) = 70.14
Respond to this Question
Similar Questions

Algebra
THe function h(t)=16t^2+v0t+h0 describes the height in feet above the ground h(t) of an object thrown vertically from a height of h0 feet, with an initial velocity of v0 feet per second, if there is no air friction and t is the time … 
Algebra
THe function h(t)=16t^2+v0t+h0 describes the height in feet above the ground h(t) of an object thrown vertically from a height of h0 feet, with an initial velocity of v0 feet per second, if there is no air friction and t is the time … 
Calculus
A pomegranate is thrown from ground level straight up into the air at time t=0 with velocity 128 feet per second. Its height in feet at t seconds is f(t)=16t^2+128t. Find the time its hits the ground and the time it reaches its highest … 
math
using this information: if an object is thrown straight up into the air from the height H feet per second then at time tseconds the height of the object is 16.1t^2 +Vt+ H feet. This formula uses only gravitational force, ignoring … 
math
using this information: if an object is thrown straight up into the air from the height H feet per second then at time tseconds the height of the object is 16.1t^2 +Vt+ H feet. This formula uses only gravitational force, ignoring … 
math. can someone explain this!
using this information: if an object is thrown straight up into the air from the height H feet per second then at time tseconds the height of the object is 16.1t^2 +Vt+ H feet. This formula uses only gravitational force, ignoring … 
calculus
A stone is thrown straight down from the edge of a roof, 750 feet above the ground, at a speed of 7 feet per second. A. Remembering that the acceleration due to gravity is 32 feet per second squared, how high is the stone 5 seconds … 
math
An object that is falling or vertically projected into the air has it height, in feet, above the ground given by the formula below, where s is the height in feet, Vo is the original velocity of the object, in feet per second, t is … 
math/physics
A pomegranate is thrown from ground level straight up into the air at time t = 0 with velocity 96 feet per second. Its height at time t seconds is f(t) = −16t2 + 96t. a) Find the time it hits the ground. t=? 
physics/calculus
A stone is thrown straight up from the edge of a roof, 600 feet above the ground, at a speed of 12 feet per second. A. Remembering that the acceleration due to gravity is 32 feet per second squared, how high is the stone 6 seconds …