Question

Hello,
A projectile is launched straight up from the ground with an initial velocity of 320 ft/sec.

a. When will the projectiles height above the ground be 1024 ft?

For this I got 16 seconds

b. When will the height of the projectile be at least 24 ft?

I am not sure how to figure this one out.

c. When will the object strike the ground?

I got 20 seconds

d. What is the maximum height of the projectile?

I got 1600 feet.

So, I am still unsure about b and I wanted to know if my other answers seem correct

Thanks

Answer 1

c) and d) are correct

for a) and the others I assume you used Calculus and the equation
distance = -16t^2 + 320t to find your answers
you must have set 1024 = -16t^2 + 320t
after re-arranging and dividing by 16 this would give you
t^2 - 20t + 64 = 0
(t-16)(t-4) = 0
so t = 16 or t = 4

you had the t=16, but failed to show the t=4 case.
It reached a height of 1024 twice, at 4 seconds after liftoff on its way up, and then 16 seconds later on its way down

for b)
set 24 = -16t^2 + 320t
16t^2 - 320t + 24 = 0
2t^2 - 40t + 3 = 0
using the quadratic formula
t = (40 ± √(1600-4(2)(3))/4
= 19.92 or .075

so between the times of .075 and 19.92 seconds the object is at least 24 feet high.

Answer 2

My mistake. b should have asked at least 1024 ft. So does that mean the answer would be anytime in between 4 and 16 seconds?

b. When will the height of the projectile be at least 1024 ft?