Standing on the roof of a (42.0+A) m tall building, you throw a ball straight up with an initial speed of (14.5+B) m/s. If the ball misses the building on the way down, how long will it take from you threw the ball until it lands on the ground below? Give your answer in seconds and round the answer to three significant figures.
A=9, B=8

Question

Standing on the roof of a (42.0+A) m tall building, you throw a ball straight up with an initial speed of (14.5+B) m/s. If the ball misses the building on the way down, how long will it take from you threw the ball until it lands on the ground below? Give your answer in seconds and round the answer to three significant figures.
A=9, B=8

simplixity · Answer

(42.0+A)= 51m

simplixity · Answer

(14.5+8)= 22.5 m/s

simplixity · Answer

I just need help with what equation to use..

jim_thompson5910 · Answer

The equation you'll use is

$$\Large y = -4.9x^2 + v*x + h$$

y = height of object in meters at time x
x = time in seconds
v = initial speed
h = initial height

In this case,
v = 22.5
h = 51

So we'll have this equation
$$\Large y = -4.9x^2 + 22.5x + 51$$
after you plug in the given info

jim_thompson5910 · Answer

`how long will it take from you threw the ball until it lands on the ground below? `
set the height to zero then solve for x

ie, replace y with 0 then isolate x

jim_thompson5910 · Answer

you'll use the quadratic formula

simplixity · Answer

okay, hang on let me do the math.. is it okay if you check my answer after?

jim_thompson5910 · Answer

sure that sounds like a good plan

simplixity · Answer

so this is how I set it up using the quadratic formula:
$$\frac{-22.5 \pm \sqrt{22.5-4(-4.9)(51)} }{ 2(-4.9)}$$

jim_thompson5910 · Answer

see attached

simplixity · Answer

so would then
$$\frac{ -22.9 \pm \sqrt{1022.1} }{ -9.8}$$
correct? or no

simplixity · Answer

oh wait I just saw your message

simplixity · Answer

so in the sqrt would be 1505.85?

jim_thompson5910 · Answer

yes `1505.85` is under the square root when you simplify

simplixity · Answer

okay so what would I do next?

jim_thompson5910 · Answer

so we'll have this
$$\Large x = \frac{-22.5 \pm \sqrt{1505.85}}{-9.8}$$

jim_thompson5910 · Answer

what is the square root of 1505.85 equal to?

simplixity · Answer

38.8053

simplixity · Answer

I think I know what to do

jim_thompson5910 · Answer

ok tell me what two solutions you get

simplixity · Answer

I got -1.66 and 6.26 but I rounded them to the third sig fig

jim_thompson5910 · Answer

Ignore -1.66

why? because x = -1.66 makes no sense. Recall that x is the time in seconds. We can't have a negative time value

jim_thompson5910 · Answer

So the only solution is x = 6.26

simplixity · Answer

oh okay, thank you!

jim_thompson5910 · Answer

you're welcome