Answer to Question #306991 in Mechanics | Relativity for Vince

Question

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?

Answer 1

Solution.

$8. v=7.6 m/s;$

$L=8.7m;$

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

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

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

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

$9.y_0=20m;$

$v=12 m/s;$

$\alpha=45^o;$

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

$0=20+12\sdot sin45^ot-\dfrac{9.8\sdot t^2}{2};$

$t=3.06s;$

$L=v_{ox}t;$

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

$v_{y}=v_{0y}-gt;$

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

Answer: $8.h=10.16m;$

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