Question

Problem 1: A soccer ball is kicked horizontally off a 22.0-meter high hill and lands a distance of 35.0 meters from the edge of the hill. Determine the initial horizontal velocity of the soccer ball. 

Problem 2: A long jumper leaves the ground with an initial velocity of 12 m/s at an angle of 28-degrees above the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the long-jumper.

Answer 1

Problem 1: the initial velocity is

$$v=R/t=R/\sqrt{2h/g}=16.5\text{ m/s}.$$

Problem 2: the time of flight, the horizontal distance, and the peak height:

$$t=\frac{2v\sin\theta}{g}=1.15\text{ s},\\\space\\ R=\frac{v^2\sin(2\theta)}{g}=12.2\text{ m},\\\space\\ H=\frac{v^2\sin^2\theta}{2g}=1.62\text{ m}.$$