An object is thrown straight up from the top of a 100-foot platform at a velocity of 48 feet per second. The height h(t) of the object t seconds after being thrown is given by.=r Find the maximum height reached by the object and the time it takes to achieve this height.

Explanation:

1. Function for the height (given):

2. Type of function

That is a quadatic function, whose graph is a parabola that opens downward.

The maximum of the function, i.e. the maximum height, is the vertex of the parabola.

The vertex of a parabola with the genral equation    is at the x-coordinate

3. Time to achieve the maximum height

Substitute b with 48 and a with - 16:

Then, time when the object achieves the maximum height it 1.5s

4. Maximum height:

Replace t with 1.5 in the equation, to find the maximum height, h(1.5)

Then, the maximum height is 136 ft

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

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step-by-step explanation: