Answer to Question #350234 in Calculus for james

Question #350234

A rock is thrown horizontally from the top of a cliff 88 m high, with a horizontal speed of 25 m/s. with what velocity does the rock hit


1
Expert's answer
2022-06-13T16:20:47-0400
"x(t)=v_{0x}t"

"y(t)=h+0\\cdot t-\\dfrac{gt^2}{2}"

"v_y(t)=y'(t)=-gt"

The rock hits the land: "y(t_1)=0."


"h-\\dfrac{gt_1^2}{2}=0, t_1\\ge0"

"t_1=\\sqrt{\\dfrac{2h}{g}}"

"v_y(t_1)=-g\\sqrt{\\dfrac{2h}{g}}=-\\sqrt{2gh}"

"|v(t_1)|=\\sqrt{v_{0x}^2+(-\\sqrt{2gh})^2}"

"=\\sqrt{v_{0x}^2+2gh}"

"=\\sqrt{(25m\/s)^2+2(9.81m\/s^2)(88m)}"

"=48.493m\/s"

"\\tan \\theta=-\\dfrac{\\sqrt{2gh}}{v_{0x}}=-\\dfrac{\\sqrt{2(9.81m\/s^2)(88m)}}{25m\/s}"

"\\approx-1.662"

"\\theta\\approx121\\degree"

The rock hits the land with the velocity 48.493 m/s at the angle "121\\degree" with respect to the ground.


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