Start your trial now! First week only \( \$ 4.99 \) ! A projectile is fired at an initial slope of 4 vertical to 3 horizontal. It reached the maximum height \( 8 \mathrm{~m} \) away from the origin and hits the ground that is \( 2 \mathrm{~m} \) bellow the origin. 7.1. Calculate the the initial velocity. a. \( 11.79 \mathrm{~m} / \mathrm{s} \) b. \( 12.78 \mathrm{~m} / \mathrm{s} \) c. \( 10.18 \mathrm{~m} / \mathrm{s} \) d. \( 13.45 \mathrm{~m} / \mathrm{s} \) 7.2. Find the maximum height reached by the said projectile a. \( 5.33 \mathrm{~m} / \mathrm{s} \) b. \( 6.12 \mathrm{~m} / \mathrm{s} \) c. \( 4.78 \mathrm{~m} / \mathrm{s} \) d. \( 5.13 \mathrm{~m} / \mathrm{s} \) 7.3. Find the range of the same. a. \( 20.11 \mathrm{~m} \) b. \( 19.62 \mathrm{~m} \) c. \( 6.27 \mathrm{~m} \) d. \( 17.39 \mathrm{~m} \) Transcribed Image Text: A projectile is fired at an initial slope of 4 vertical to 3 horizontal. It reached the maximum height \( 8 \mathrm{~m} \) away from the origin and hits the ground that is \( 2 \mathrm{~m} \) bellow the origin. 7.1. Calculate the the initial velocity. a. \( 11.79 \mathrm{~m} / \mathrm{s} \) c. \( 10.18 \mathrm{~m} / \mathrm{s} \) b. 12.78
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A projectile is launched from the point $(x=0, y=0)$, with velocity $(12.0 \mathrm{i}+49.0 \mathrm{j}) \mathrm{m} / \mathrm{s},$ at $t=0 .$ (a) Make a table listing the projectile's distance $|\overrightarrow{\mathrm{r}}|$ from the origin at the end of each second thereafter, for $0 \leq t \leq 10 \mathrm{s}$ . Tabulating the $x$ and $y$ coordinates and the components of velocity $v_{x}$ and $v_{y}$ will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the velocity. Suggestion: Argue that if $\vec{v}$ is not perpendicular to $\overrightarrow{\mathbf{r}},$ then $|\overrightarrow{\mathbf{r}}|$ must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain your method for solving part (c).
(II) A projectile is shot from the edge of a cliff 125 $\mathrm{m}$ above ground level with an initial speed of 65.0 $\mathrm{m} / \mathrm{s}$ at an angle of $37.0^{\circ}$ with the horizontal, as shown in Fig. $3-35$ . (a) Determine the time taken by the projectile to hit point P at ground level. ( $b )$ Determine the range $X$ of the projectile as measured from the base of the cliff. At the instant just before the projectile hits point $P$ , find $(c)$ the horizontal and the vertical components of its velocity, $(d)$ the magnitude of the velocity, and $(e)$ the angle made by the velocity vector with the horizontal. $(f)$ Find the maximum height above the cliff top reached by the projectile.
A projectile is launched from the point $(x=0, y=0)$ with velocity $(12.0 \hat{\mathrm{i}}+49.0 \mathrm{j}) \mathrm{m} / \mathrm{s},$ at $t=0$ (a) Make a table listing the projectile's distance $|\overrightarrow{\mathbf{r}}|$ from the origin at the end of each second thereafter, for $0 \leq t \leq$ 10 s. Tabulating the $x$ and $y$ coordinates and the components of velocity $v_{x}$ and $v$, will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the velocity. Suggestion: Argue that if $\overrightarrow{\mathrm{v}}$ is not perpendicular to $\overrightarrow{\mathbf{r}},$ then $|\overrightarrow{\mathbf{r}}|$ must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain your method for solving part (c).
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