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A ball is shot from a cannon into the air. The equation that's gives the height (h) of the ball of any time (t) is: h(t)= -16t^2 + 40t + 1.5

Respuesta :

Answer:

26.5 units

Step-by-step explanation:

The height of the ball at any time t is given by :

[tex]h(t)= -16t^2 + 40t + 1.5[/tex] ...(1)

We need to find the maximum height of the ball.

For maximum height, put [tex]\dfrac{dh}{dt}=0[/tex]

i.e.

[tex]\dfrac{d( -16t^2 + 40t + 1.5)}{dt}=0\\\\-32t+40=0\\\\t=\dfrac{40}{32}\\\\t=1.25\ s[/tex]

Put t = 1.25 in equation (1) to find the maximum height.

So,

[tex]h(t)= -16(1.25)^2 + 40(1.25) + 1.5\\\\=26.5\ units[/tex]

So, the maximum height reached by the ball is 26.5 units.

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