Answer to Question #306991 in Mechanics | Relativity for Vince

Question #306991

8. A ball rolls horizontally with a speed 0f 7.6 m/s off the edge of a tall platform. If the ball lands 8.7 m from the point on the ground directly below the edge of the platform, what is the height of the platform?



9. A stone thrown off a bridge 20 m above a river has an initial velocity of 12 m/s at an angle of 45° above the horizontal.


What is the range of the stone?


At what velocity does the stone strike the water?



1
Expert's answer
2022-03-15T16:50:08-0400

Solution.

8.v=7.6m/s;8. v=7.6 m/s;

L=8.7m;L=8.7m;

L=vt    t=Lv;L=vt\implies t=\dfrac{L}{v};

t=8.77.6=1.44s;t=\dfrac{8.7}{7.6}=1.44s;

h=gt22;h=\dfrac{gt^2}{2};

h=9.81.4422=10.16m;h=\dfrac{9.8\sdot1.44^2}{2}=10.16m;

9.y0=20m;9.y_0=20m;

v=12m/s;v=12 m/s;

α=45o;\alpha=45^o;

y=yo+v0ytgt22;y=y_o+v_{0y}t-\dfrac{gt^2}{2};

0=20+12sin45ot9.8t22;0=20+12\sdot sin45^ot-\dfrac{9.8\sdot t^2}{2};

t=3.06s;t=3.06s;

L=voxt;L=v_{ox}t;

L=120.70713.06=26m;L=12\sdot0.7071\sdot3.06=26m;

vy=v0ygt;v_{y}=v_{0y}-gt;

vy=120.70719.83.06=21.5m/s;v_y=12\sdot0.7071-9.8\sdot3.06=-21.5m/s;

Answer: 8.h=10.16m;8.h=10.16m;

9.L=26m;vy=21.5m/s.9. L=26m; v_y=-21.5 m/s.









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