In Exercises 39 and 40, use the following fact derived from...

In Exercises 39 and 40, use the following fact derived from Newton's Laws: An object released at an angle $\theta$ with initial velocity $v$ fu/s travels a horizontal distance $$ s=\frac{1}{32} v^2 \sin 2 \theta \mathrm{ft} \text { (Figure 10) } $$ A player located 18.1 ft from the basket launches a successful jump shot from a height of 10 ft (level with the rim of the basket), at an angle $\theta=34^{\circ}$ and initial velocity $v=25 \mathrm{ft} / \mathrm{s}$.) (a) Show that $\Delta s \approx 0.255 \Delta \theta$ ft for a small change of $\Delta \theta$. (b) Is it likely that the shot would have been successful if the angle had been off by $2^{\circ}$ ? ( figure can't copy )

In Exercises 39 and 40, use the following fact derived from Newton's Laws: An object released at an angle $\theta$ with initial velocity $v$ fu/s travels a horizontal distance
$$
s=\frac{1}{32} v^2 \sin 2 \theta \mathrm{ft} \text { (Figure 10) }
$$
A player located 18.1 ft from the basket launches a successful jump shot from a height of 10 ft (level with the rim of the basket), at an angle $\theta=34^{\circ}$ and initial velocity $v=25 \mathrm{ft} / \mathrm{s}$.)
(a) Show that $\Delta s \approx 0.255 \Delta \theta$ ft for a small change of $\Delta \theta$.
(b) Is it likely that the shot would have been successful if the angle had been off by $2^{\circ}$ ?
( figure can't copy )

In Exercises 47 and 48 , use the following fact derived from Newton's Laws: An object released at an angle $\theta$ with initial velocity v $\mathrm{ft} / \mathrm{s}$ travels a horizontal distance $$ s=\frac{1}{32} v^{2} \sin 2 \theta \mathrm{ft} \text { (Figure } $$ A player located $18.1 \mathrm{ft}$ from the basket launches a successful jump shot from a height of $10 \mathrm{ft}$ (level with the rim of the basket), at an angle $\theta=34^{\circ}$ and initial velocity $v=25 \mathrm{ft} / \mathrm{s}$ (a) Show that $\Delta s \approx 0.255 \Delta \theta \mathrm{ft}$ for a small change of $\Delta \theta$. (b) Is it likely that the shot would have been successful if the angle had been off by $2^{\circ}$ ? (c) Estimate $\Delta s$ if $\theta=34^{\circ}, v=25 \mathrm{ft} / \mathrm{s},$ and $\Delta v=2$.

Applications of the Derivative

Linear Approximation and Applications

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