do question 16 13. A stone is thrown upward from ground level. The initial speed

Question

do question 16

13. A stone is thrown upward from ground level. The initial speed is 128 feet per second. How 14. A stone is thrown upward from ground level. With what minimum speed should the stone be 15. A falling stone is at a certain instant 158 feet above the ground and 2 seconds later it is only 16. A falling stone is at a certain instant 90 feet above the ground. Two seconds later it is only high will it go? thrown so as to reach a height of 49 feet? 14 feet above the ground. From what height was it dropped? 10 feet above the ground. If it was thrown down with an initial speed of 4 feet per second, from what height was it thrown? 17. A falling stone is at a certain instant 100 feet above the ground. Two seconds later it is only 20 feet above the ground. If it was thrown upward with an initial speed of 7 feet per second from what height was it thrown?

Explanation / Answer

S(t) = So + Vot - At²/2

S(t) = 90 = So - 4t - 16.1t² …………………………….( 1 )
S(t+2) = 10 = So - 4(t+2) - 16.1(t+2)²

10 = So - 4t - 8 - 16.1(t² + 4t + 4)
10 = So - 4t - 8 - 16.1t² - 64.4t - 64.4
10 + 8 + 64.4 = So - 68.4t - 16.1t²

82.4 = So – 68.4t - 16.1t² ………………………………( 2 )
solve equation ( 1 ) & ( 2 )

So -   4t    - 16.1t² = 90
So – 68.4t - 16.1t² = 82.4
64.4t = 7.6
t = 7.6/64.4 = .11801

90 = So - 4(.11801) - 16.1(.11801)²

So = 90.6962 ft.
The stone was thrown from a height of 90.6962 ft

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