Question

HELP!!

A rocket is shot upward from the surface of the earth at an initial velocity of 200 ft/sec. When will the projectile FIRST reach a height of 600 ft?

Use the equation h(t)=-16t^2+v(sub 0)t+h(sub 0) where v(sub 0) is the initial velocity and h(sub 0) is the initial height

Answer 1

\[h(t)=-16t ^{2}+v _{0}t+h _{0}\]

Answer 2

I've never done a problem like this before

Answer 3

It is given to you that :

\(v_0 = 200 \space ft/sec\)

h(t) = 600 ft.

h(0) = 0 (as it is thrown upwards from the surface)

Answer 4

Just plug-in these values in the equation and solve for "t" . Can you do that?

Answer 5

t = 5, 15/2! So it would be 5 seconds?

Answer 6

Yeah, it would be 5 & 7.5 sec.

Answer 7

Thank you so much! If you have a little time could you help me with one last problem?

Answer 8

A football player is practicing kicking field goals with the ball on the 25 yard line (105ft from the goalposts). If you imagine a coordinate system with the ball being kicked at d=0 and the goal post at d=105, then the equation of the ball's path is h(d)=-1/90(d-60)^2 + 40 where h is the ball's height in feet.

A. What is the maximum height of the ball
B. What will the height of the ball be when it reaches the goal-post crossbar which is 10ft above the ground.

Answer 9

Mighty , sorry for late reply! We'll use maxima and minima here (to calculate the max. height of the ball)

I assume that the equation is :

h(d) = \(\cfrac{-1}{90} (d-60)^2 + 40\)

Differentiate this :

h'(d) = \(\cfrac{-2}{90} (d-60) \) = 0 ----------(1)
So,
d = 60 ft. and h(d) = \(\cfrac{-1}{90}(60-60)^2 + 40 = 40 \space ft.\)

Now differentiate the eq. 1 again

h''(d) = \(\cfrac{-2}{90}\) --------------------(2)

As from equation (2) , h''(d) < 0

Therefore, it is clear that h(d) = 40 ft. is the maximum height of the ball.

For the B) Part, I am not sure. If the ball reaches the goal post crossbar (which is 10 ft.above the ground) , so the height of the ball from the ground should be 10 ft. too ! I am not sure if I correctly understood this part or not!

Answer 10

Oh, they want to know the height of the ball when it travels directly over the crossbar (150ft away from where it was first kicked). Is that what you thought? 10 ft could be a possible answer though I think! @mathslover

Answer 11

150 or 105?

Answer 12

Sorry 105ft is correct! Typing too fast

Answer 13

No problem , was just verifying :) I still think it is 10 ft. , it will be great if you please verify this part with your teacher.. :)

Answer 14

I will! After class I'll come back on here and let you know how I did with these two problems! Again thank you so much, you're a lifesaver!

Answer 15

You're welcome. Sorry for not helping you with part B) .. :(