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aleksandrvk [35]
3 years ago
7

If a ball is thrown directly upward with a velocity of 50ft/s, it's height (in feet) after t seconds is given by y=50t-16t^2 wha

t is the maximum height attained by the ball
Mathematics
1 answer:
Tomtit [17]3 years ago
7 0

Answer:

39.0625 ft

Step-by-step explanation:

Since the function is a quadratic representing height, and the coefficient of the t² is negative, the vertex of the parabola will be the maximum height achieved by the ball.  

The general form for a quadratic equation is ax² + bx + c, here a is -16, and b is 50

To find the x coordinate of the vertex, use   x = -b/(2a)

We have x = -50/[2(-16)]

               

                  x = -50/-32

             

                         x= 25/16

Now plug that into the equation to find the y value, which will be the height...

y = 50(25/16) - 16(25/16)²

    y = 1250/16 - 16(625/256)

        y = 1250/16 - 625/16

              y = 625/16

                   y = 39.0625

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yan [13]

Answer:

Part a) Ernest's calculation was correct

Part b) Ernest's calculation was correct

Step-by-step explanation:

The picture of the question in the attached figure

<u><em>The complete question is</em></u>

Ernest calculated the slope of the graph during the uphill climb to be 10. His work is shown below.

Points: (60.900). (15, 450)

Slope : 900-450/60-15=450/45=10

Part a) Determine whether his calculation was correct or incorrect, and then explain why.

Part b) Confirm or disprove Ernest's work by selecting two different points and applying the slope formula. be sure to identify the points you chose

Part a)

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

we have the points

A(60,900),B(15,450)

Remember that

m_A_B=m_B_A

step 1

Find m_A_B

substitute in the formula

m_A_B=\frac{450-900}{15-60}\\\\m_A_B=\frac{-450}{-45}=10

step 2

Find m_B_A

substitute in the formula

m_B_A=\frac{900-450}{60-15}\\\\m_B_A=\frac{450}{45}=10

therefore

Ernest's calculation was correct, because m_A_B=m_B_A

Part b) selecting two different points

we take the points

(0,300) and (50,800) -----> see the attached figure

substitute in the formula of slope

m=\frac{800-300}{50-0}

m=\frac{500}{50}

m=10

therefore

Ernest's calculation was correct

8 0
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