<span>Your equation for the height of the stone at any time is h(t) = -16t2<span> + 128t + 32 .
From your equation, we can tell that you're defining the upward direction as
positive. We can also tell that you threw the stone upward, with an initial speed
as it left your hand of 128 feet per second, about 87 miles per hour ... a mighty toss indeed, and I think there's a man from the Chicago Cubs waiting outside
who'd like to talk to you.
Anyway, When the stone splashes into the water, h(t) = 0 .
</span></span>
<span>-16t²<span> + 128t + 32 = 0</span></span>
Divide each side by -16 :
t² - 8t - 2 = 0
I don't see any easy way to factor the expression on the left,
so I have to use the quadratic formula to solve this equation.
t = 4 plus and minus √18 .
t = +8.24 seconds
t = -0.24 second
Mathematically, both numbers are valid solutions.But when you apply
the equation to a real world situation, only the positive 't' makes sense.
So <u> t = 8.24 seconds</u>.
Answer:
Explanation:
Important here is to know that due north is a 90 degree angle, due east is a 0 degree angle, and due south is a 270 degree angle. Then we find the x and y components of each part of this journey using the sin and cos of the angles multiplied by each magnitude:
Add them all together to get the x component of the resultant vector, V:
Do the same to find the y components of the part of this journey:
Add them together to get the y component of the resultant vector, V:
One thing of import to note is that both of these components are positive, so the resultant angle lies in QI.
We find the final magnitude:
and, rounding to 2 sig dig's as needed:
1.0 × 10² m; now for the direction:
58°
Because of the location of Mg on the periodic table.
The sun is approximately 27,000 light years away from the center of our galaxy.
