Marting throws a baseball upwards at a velocity of 80 ft/sec. The following equation models this situation: H (t) = -16t squared + 80t + 6 , where H(t) is the height of the ball in feet and t is the time in seconds after the ball was released. HOW LONG WILL IT TAKE THE BALL TO REACH ITS PEAK (highest point)?
If the ball takes 2.5 secs to reach its highest point what is the maximum height the ball will travel? 102ft 106ft 2ft OR 180ft
How high will the ball hit in 4secs? 102ft 0ft -90ft OR 70ft
Kiki, I found the 2.5 seconds for you in your previous post.
Just sub that value into your equation.
then do it again for t = 4
let me know what you got.
Im not understanding this at all.
To find out how long it will take for the ball to reach its peak, we need to find the time when the velocity of the ball becomes zero. At the highest point, the velocity of the ball will be zero.
We are given the equation H(t) = -16t^2 + 80t + 6 to represent the height of the ball at time t.
To find the time it takes for the ball to reach its peak, we need to find the value of t that makes the velocity zero.
The velocity is the derivative of the height function with respect to time, which is given by V(t) = dH/dt.
Let's calculate the derivative of the height function. The derivative of -16t^2 + 80t + 6 is -32t + 80.
Since we want to find when the velocity is zero, we set -32t + 80 = 0.
Solving the equation, we have:
-32t + 80 = 0
-32t = -80
t = -80 / -32
t = 2.5
So it will take the ball 2.5 seconds to reach its peak.
To find the maximum height the ball will travel, we can substitute the value of t = 2.5 into the height function H(t).
H(2.5) = -16(2.5)^2 + 80(2.5) + 6
H(2.5) = -16(6.25) + 200 + 6
H(2.5) = -100 + 200 + 6
H(2.5) = 106
Therefore, the maximum height the ball will travel is 106 feet.
Now, let's find out how high the ball will be at 4 seconds. We can use the same procedure and substitute t = 4 into the height function H(t).
H(4) = -16(4)^2 + 80(4) + 6
H(4) = -16(16) + 320 + 6
H(4) = -256 + 320 + 6
H(4) = 70
So the ball will hit at a height of 70 feet after 4 seconds.