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Sagot :
Answer:
The ball will hit the ground at 10 seconds and its maximum height is 1024 feet.
Step-by-step explanation:
Height of a mountain, h = 90 feet
Upward velocity of a ball, u = 64 ft/s
Its height as a function of time can be written by using the second equation of motion as follows :
[tex]f(x) = -16t^2 + 64t + 960[/tex] .....(1)
When it will hit the ground, f(x) = 0
[tex]-16t^2 + 64t + 960=0\\\\16(-t^2+4t+60)=0\\\\-t^2+4t+60=0[/tex]
It is quadratic equation.
t = -6 s and t = 10 s
Neglecting -6 seconds, the ball will hit the ground at 10 seconds.
For maximum height,
Put f'(x) = 0
[tex]-32t+64=0\\\\\\t=\dfrac{64}{32}\\\\t=2\ s[/tex]
Put t = 2 in equation (1)
[tex]f(2) = -16(2)^2 + 64(2) + 960\\\\=1024\ \text{feet}[/tex]
Hence, the ball will hit the ground at 10 seconds and its maximum height is 1024 feet.
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