Question

a stone of weight W is thrown vertically upward with speed V' from ground level.a constant force f acting due to drag of air in its flight .the maximum height will be...

Answer 1

Answer on Question #51614 – Physics – Mechanics | Kinematics | Dynamics

A stone of weight $W$ is thrown vertically upward with speed $V'$ from ground level. A constant force $f$ acting due to drag of air in its flight. The maximum height will be...

Solution.

We write down an equation of motion:

$$dp/dt = F_{tot}$$ $$md^2/dx^2 = -mg - ma$$

Since $a \neq a(v)$,

$$x = -(g + a)t^2/2 + v_0 t + x_0,$$

$x_0 = 0$, and $x_{max} =$ his reached when the velocity is zero

$$dx/dt = 0 = -(g + a)t + v_0$$ $$t_{top} = v_0/(g + a)$$

Putting $t_{top}$ in the final equation, we obtain

$$h = -(g + a)v_0^2/2(g + a)^2 + v_0^2/(g + a) = \frac{v_0^2}{2(g + a)}$$

Answer.

$$h = \frac{v_0^2}{2(g + a)}$$

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