Please help !
1.)a catapult launches a boulder with an upward velocity of 122 feet per second. the height of the boulder, h, in feet after t seconds is givin by the function h(t)=-16t^2+122t+10. what is the boulders maximum height ? and how long does it take the boulder to reach its maximum height ? round to the nearest hundredth if necessary.
a.)reaches a maximum height of 15.42 feet after 7.71 seconds
b.)reaches a maximum height of 7.71 feet after 3.81 seconds
c.)reaches a maximum height of 242.56 feet after 7.62 seconds
d.) reaches a maximum height of 242.56 feet after 3.81 seconds.
2.)a ball is thrown with a upward velocity of 28 ft/s. its height h, in feet after t seconds is given by the function h=-16t^2+28t+7. what is the balls maximum height how long does it take the ball to reach maximum height ? round to the nearest hundredth if needed.
a.)reaches a maximum height of 7 feet after 1.75 seconds
b.) reaches a maximum height of 43.75 feet after 0.88 seconds
c.)reaches a maximum height of 17.5 feet after 0.88 seconds
d.)reaches a maximum height of 19.25 feet after 0.88 seconds
the answer for #1 is "reaches a maximum height of 242.56 feet after 3.81 seconds." 2022
SSUUUIIIIIIIIII
Sure, I'd be happy to help you with these problems! Let's go through them one by one:
1.) To find the maximum height of the boulder, we need to find the vertex of the quadratic function h(t) = -16t^2 + 122t + 10. The formula for finding the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is -b/2a. In this case, a = -16 and b = 122. Plugging these values into the formula, we get t = -122 / (2 * -16) = 7.62 seconds.
Now, to find the maximum height, we substitute this value of t back into the function. So, h(7.62) = -16(7.62)^2 + 122(7.62) + 10 = 242.56 feet.
So, the boulder reaches a maximum height of 242.56 feet after 7.62 seconds.
Answer: c.) reaches a maximum height of 242.56 feet after 7.62 seconds.
2.) Similar to the previous problem, to find the maximum height of the ball, we need to find the vertex of the quadratic function h(t) = -16t^2 + 28t + 7. Again, using the formula -b/2a, we get t = -28 / (2 * -16) = 0.875 seconds.
Now, substituting this value back into the function, we get h(0.875) = -16(0.875)^2 + 28(0.875) + 7 = 19.25 feet.
So, the ball reaches a maximum height of 19.25 feet after 0.875 seconds.
Answer: d.) reaches a maximum height of 19.25 feet after 0.875 seconds.
Hope this helps! Let me know if you have any more questions.
To find the maximum height of the boulder and the time it takes to reach that maximum height, we need to analyze the given quadratic function h(t)=-16t^2+122t+10.
1.) Maximum Height of the Boulder:
The maximum height of the boulder corresponds to the vertex of the parabolic function. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic function in the form ax^2 + bx + c.
In our case, the quadratic function is h(t) = -16t^2 + 122t + 10, and therefore, the coefficient of t^2 is -16 and the coefficient of t is 122. Plugging these values into the formula, we have:
t = -122 / (2 * (-16))
t ≈ 7.71 seconds
Now, to find the maximum height, we substitute this value of t into the function h(t):
h(7.71) = -16 * (7.71)^2 + 122 * 7.71 + 10
h(7.71) ≈ 15.42 feet
Therefore, the boulder reaches a maximum height of 15.42 feet after 7.71 seconds. So, the correct answer is option a.) reaches a maximum height of 15.42 feet after 7.71 seconds.
2.) Maximum Height of the Ball:
Similar to the previous question, the maximum height of the ball corresponds to the vertex of the quadratic function h(t) = -16t^2 + 28t + 7.
Using the same formula as before, x = -b / (2a), we can calculate the time it takes for the ball to reach the maximum height:
t = -28 / (2 * (-16))
t ≈ 0.88 seconds
Substituting this value of t into the function h(t), we can find the maximum height:
h(0.88) = -16 * (0.88)^2 + 28 * 0.88 + 7
h(0.88) ≈ 19.25 feet
Therefore, the ball reaches a maximum height of 19.25 feet after 0.88 seconds. So, the correct answer is option d.) reaches a maximum height of 19.25 feet after 0.88 seconds.
Number 2 is D. yw :)
Remember your Algebra I. The max height is represented by the vertex of the parabola. As with all quadratics, the vertex is at t = -b/2a. So, for
#1: t = -122/-32 = 3.8125 seconds
use the same logic on #2.