Answer to Question #289084 in Physics for Mozai

Question

In the middle of the night, you are standing a horizontal distance of 14.0 m from the high fence that surrounds the estate of your rich uncle. The top of the fence is 5.00 m above the ground. You have taped an important message to a rock that you want to throw over the fence. The ground is level, and the width of the fence is small enough to be ignored. You throw the rock from a height of 1.60 m above the ground and at an angle of 56.0o above the horizontal. (a) What minimum initial speed must the rock have as it leaves your hand to clear the top of the fence? (b) For the initial velocity calculated in part (a), what horizontal distance beyond the fence will the rock land on the ground?

Answer 1

(a) The initial velocity must suffice the following requirement:

$$v\cos\theta·t=x,\\ t=\sqrt\dfrac{2(H-h)}g,\\\space\\ v\cos\theta·\sqrt\dfrac{2(H-h)}g=x,\\\space\\ v=\dfrac x{\cos\theta·\sqrt{2(H-h)/g}},\\\space\\ v=\dfrac {14}{\cos56·\sqrt{2(5-1.6)/9.8}}=30\text{ m/s}.$$

(b) The horizontal distance here is

$$l=v\cos\theta·t_2,\\\space\\ t_2=\sqrt\dfrac{2H}g,\\\space\\ l=v\cos\theta·\sqrt\dfrac{2H}g=17\text{ m}.$$