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)=v0xtx(t)=v_{0x}t

y(t)=h+0tgt22y(t)=h+0\cdot t-\dfrac{gt^2}{2}

vy(t)=y(t)=gtv_y(t)=y'(t)=-gt

The rock hits the land: y(t1)=0.y(t_1)=0.


hgt122=0,t10h-\dfrac{gt_1^2}{2}=0, t_1\ge0

t1=2hgt_1=\sqrt{\dfrac{2h}{g}}

vy(t1)=g2hg=2ghv_y(t_1)=-g\sqrt{\dfrac{2h}{g}}=-\sqrt{2gh}

v(t1)=v0x2+(2gh)2|v(t_1)|=\sqrt{v_{0x}^2+(-\sqrt{2gh})^2}

=v0x2+2gh=\sqrt{v_{0x}^2+2gh}

=(25m/s)2+2(9.81m/s2)(88m)=\sqrt{(25m/s)^2+2(9.81m/s^2)(88m)}

=48.493m/s=48.493m/s

tanθ=2ghv0x=2(9.81m/s2)(88m)25m/s\tan \theta=-\dfrac{\sqrt{2gh}}{v_{0x}}=-\dfrac{\sqrt{2(9.81m/s^2)(88m)}}{25m/s}

1.662\approx-1.662

θ121°\theta\approx121\degree

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


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS