Mariano is standing at the top of a hill when he kicks a soccer ball into the air. The height of the hill is h feet, and the ball is kicked with an initial velocity of v feet per second. The height of the ball above the bottom of the hill after t seconds is given by the polynomial -16t2 + vt + h. Find the height of the ball after 2 seconds if it is kicked from the top of a 60 foot tall hill at 84 feet per second.
Well, Mariano certainly knows how to kick a ball! Let's plug in the values into the polynomial and find out the height of the ball after 2 seconds.
We have h = 60 (since the hill is 60 feet tall) and v = 84 (the initial velocity is 84 feet per second). So the polynomial becomes:
-16t^2 + vt + h
Plugging in t = 2, we get:
-16(2)^2 + 84(2) + 60
Solving this equation, we get:
-16(4) + 168 + 60
-64 + 168 + 60
104 + 60
So, after 2 seconds, the height of the ball above the bottom of the hill is 164 feet. That's quite a kick!
To find the height of the ball after 2 seconds, we need to substitute the given values into the equation -16t^2 + vt + h and solve for the height (h) when t = 2.
Given:
Initial height of the hill (h) = 60 feet
Initial velocity (v) = 84 feet per second
Time (t) = 2 seconds
Substituting these values into the equation:
Height (h) = -16t^2 + vt + h
Height (h) = -16(2)^2 + 84(2) + 60
Now, we'll calculate:
Height (h) = -16(4) + 168 + 60
Height (h) = -64 + 168 + 60
Height (h) = 104 + 60
Height (h) = 164 feet
So, the height of the ball after 2 seconds, if it is kicked from the top of a 60-foot tall hill at 84 feet per second, is 164 feet.
It's 57. Plug in the numbers into the equation given with the variables listed.
thanks!
just plug in your numbers:
h(t) = -16t^2 + 84t + 60
assuming he kicks it straight up.
Now just plug in t=2