Sloane kicked a soccer ball off the ground at a speed of 36 feet per second. The height of the ball can be represented by the function H(t) = −16t2 + 36t. How many seconds did the ball travel before returning to the ground?
t = 0.44 seconds
t = 2.25 seconds
t = 16 seconds
t = 36 seconds
To find when the ball returns to the ground, we need to find when H(t) = 0. So we set the function equal to 0 and solve for t:
-16t^2 + 36t = 0
Factor out t:
t(-16t + 36) = 0
Either t = 0 or -16t + 36 = 0
Solving the second equation for t:
-16t + 36 = 0
-16t = -36
t = 2.25
So the ball traveled for 2.25 seconds before returning to the ground.
Answer: t = 2.25 seconds.
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To find how many seconds the ball traveled before returning to the ground, we need to find the value of t when H(t) = 0.
Given the function H(t) = −16t^2 + 36t, we can set it equal to 0:
−16t^2 + 36t = 0
Factoring out a common factor of 4t, we get:
4t(-4t + 9) = 0
Setting each factor equal to 0 and solving for t, we have:
4t = 0 => t = 0
-4t + 9 = 0 => -4t = -9 => t = -9/-4 => t = 9/4 => t = 2.25
Therefore, the ball traveled for 0 seconds (initial position) and 2.25 seconds before returning to the ground.
To find out how many seconds the ball traveled before returning to the ground, we need to find the value of t when H(t) is equal to zero.
We can set up the equation H(t) = -16t^2 + 36t and solve for t.
-16t^2 + 36t = 0
Factoring out a common factor of 4t, we get:
4t(-4t + 9) = 0
Now we can solve for t by setting each factor equal to zero:
4t = 0 or -4t + 9 = 0
From the first equation, we find t = 0.
From the second equation, we have -4t + 9 = 0. Solving for t, we get:
-4t = -9
t = 9/4
t = 2.25
Therefore, the ball traveled for 0 seconds (at the beginning) and for 2.25 seconds before returning to the ground.
So the correct answer is t = 2.25 seconds.