Suppose a bullet is fired on a distant plant?

Question

so that it's height (in feet) after t seconds is given by h=-4t^2+16t+5
When is the bullet at its highest point?
When will the bullet strike the ground?
What is the maximum height the bullet will attain?

Answer 1

Bullet at highest point at t=2 seconds.
Bullet strikes ground at t=4.29 seconds.
Max height = 21 feet.

Answer 2

OK, I think the first and last questions have to do with maximizing H. To do that, you have to differentiate H with respect to T, the find places where the derivative is 0. The derivative of (-4t^2 + 16t + 5) is -8T +16. This is 0 when T=2. Therefore the bullet is at its highest point after 2 seconds.

I'm going to go ahead and answer the third question next. The bullet reaches its highest point after 2 seconds, and the height is -4*2^2 + 16*2 + 5 = -16 + 32 + 5 = 21 feet.

As for the second question, to solve it we need to set H = 0. -4t^2 + 16t + 5 = 0. This is a quadratic equation and can be solved through the formula x = (-b +/- sqrt(b^2 -4ac))/2a.

Plugging in the numbers gives: x = (-16 +/- sqrt(336))/-8. The square root of 336 is about 18.3, so the equation becomes: x = (-16 +/- 18.3)/-8. That means x = (2.3 OR -34.3)/-8. 2.3/-8 is a negative number, which doesn't make sense in this context, so x = -34.3/-8 = 4.2875 seconds.

Answer 3

1. The bullet is at it's highest point when it reaches the stationary point of it's parabolic trajectory (as in part 3), so the highest point will be reached after 2 seconds

2. The time it will strike the ground is calculated by factorising the equation. Therefore the bullet will strike the ground after 4.33 seconds

3. The maximum height will be the same as a stationary point on the curve of it's parabolic trajectory.

h(t) = 4t^2 + 16t + 5

The derivative, h'(t) = 8t + 16

8t + 16 = 0 for stationary points

the time is 2 seconds, so the maximum height = 11 feet

Answer 4

h=-4t^2+16t+5
h'=-8t+16
put h'=0,t=2sec
h"=-8
1]After 2 sec height is a maximum or the
bullet is at highest point
It is a maximum because second
derivative is negative.
2]Max height
=-4*4+16*2+5
=21ft.
3]We have to use the height-time relation
given to know when the bullet will hit
the ground. It should be equal to the
time it took to get to highest point.
We will compute it.
h=-4t^2+16t+5
21=-4t^2+16t+5
4t^2-16t+16=0
t^2-4t+4=0
[t-2]^2=0
t=2sec

Answer 5

Plot the function, you'll get a parabola that opens downward.
The Y axis is the height. The X axis is time. From the curve you can find the peak height (21 feet), the time (2 seconds) and the time it strikes the ground (4 sec). I did the math mentally. Hope its right. Check it.

Answer 6

No, no, no. You need to read the original question.
'Suppose a bullet is fired on a distant PLANT'
I think this should be in the Botany section.

Answer 7

Where is your velocity of the bullet?
Where is the gravity component?
Where is the bullet weight?

Can't help you with the "I shot a bullet into the air... where it lands, I know not where"

Answer 8

it depends if its a silver bullet. hi ho silver!!!