Answer:
Step-by-step explanation:
Given
Diver is standing [tex]7\ m[/tex] above water
Diver is at a maximum height of [tex]h=7+2=9\ m[/tex] at [tex]t=2\ s[/tex]
So, at [tex]t=2\ s[/tex] his velocity is zero
After this he will be under free fall
using
[tex]s=ut+\frac{1}{2}at^2[/tex]
here [tex]u=0[/tex]
[tex]s=\frac{1}{2}\times 10\times (3)^2[/tex]
[tex]s=5\times 9=45\ m\quad \text{(not possible)}[/tex]
but the distance between the pool and Henry is [tex]9\ m[/tex]
So, he reaches the pool before [tex]5\ s[/tex]
[tex]9=\frac{1}{2}\times 10\times (t)^2[/tex]
[tex]t=\sqrt{1.8}[/tex]
[tex]t=1.34\ s[/tex]
So, he reaches pool at [tex]t=2+1.34=3.34\ s[/tex] after diving off the board
Answer:
Ignore the answer above, the correct answer is 4.5m.
Step-by-step explanation:
If you ignore all the useless information, you'll see that the parabola Henry creates has a vertex of (2,9) (because obviously the parabola opens downwards). Using this, we can deduce the vertex form of the equation for this parabola to be y=-a(x-2)²+9. This is because the vertex is always equal to (h,k), and the vertex form of any parabola is written as y=a(x-h)²+k. Now, you can solve for a to find it is 0.5, by using (0,7) as the y-intercept (aka the diving board, his starting location). Now, you can graph y=-0.5(x-2)²+9 by using mapping notation, (I find to be the easiest), or any other strategy you'd like. Once graphed, it is clear to see that when the parabola reaches 5 along the x-axis, (simpler if you think of the x-axis as time and the y-axis as height), it is plotted at 4.5 on the y-axis. This means that after 5 seconds, Henry is 4.5 meters above the water.
