Suppose the stone is thrown at an angle of $25\mathrm{.}0°$ below the horizontal from the same building $(ℎ=44\mathrm{.}0\mathrm{????})$ as in the example above. If it strikes the ground $81\mathrm{.}9\mathrm{????}$ away, find the following. $($Hint: For part $($a$),$ use the equation for the $\mathrm{????}-$displacement to eliminate ${\mathrm{????}}_0\mathrm{????}$ from the equation for the $\mathrm{????}-$displacement.$)$

$($c$)$ the speed and angle of the velocity vector with respect to the horizontal at impact

What is the initial velocity? Is either component negative? Which component changes with speed time? How does it change? What equations govern the changes in the components of velocity? If you know the components of the final velocity, can you find its magnitude and direction? $\frac{\mathrm{????}}{\mathrm{????}}$

A stone is thrown upward from the top of a building at an angle of $30\mathrm{.}0°$ to the horizontal and with an initial speed of $20\mathrm{.}0\frac{\mathrm{????}}{\mathrm{????}},$ as in the figure. The point of release is $45\mathrm{.}0\mathrm{????}$ above the ground. $($a$)$ How long does it take for the stone to hit the ground? $($b$)$ Find the stone's speed at impact. $($c$)$ Find the horizontal range of the stone. Neglect air resistance.

Strategy Choose coordinates as in the figure, with the origin at the point of release. $($a$)$ Fill in the constants of the proper equation for the $\mathrm{????}-$displacement and set the displacement equal to $-45\mathrm{.}0\mathrm{????},$ the $\mathrm{????}-$displacement when the stone hits the ground. Using the quadratic formula, solve for the time. To solve part $($b$),$ substitute the time from part $($a$)$ into the components of the velocity, and substitute the same time into the equation for the $\mathrm{????}-$displacement to solve part $($c$).$

 

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To solve part c of this question we first need to find the horizontal range of the stone which is th... View the full answer