Question

A ball is kicked horizontally off a 32.0 meter high hill and lands a distance of 40.0 meters from the edge of the hill. What is the initial horizontal velocity of the soccer ball?

Answer 1

To determine the initial horizontal velocity of the soccer ball, we can use the formula for horizontal distance traveled:

$d=v_0\cdot t$,

where:

• $d$ is the horizontal distance traveled (40.0 meters in this case),
• $v_0$ is the initial horizontal velocity of the ball (the value we want to find), and
• $t$ is the time of flight.

The time of flight can be determined using the formula for vertical displacement:

$h=\frac{1}{2}g{t}^2$,

where:

• $h$ is the vertical displacement (32.0 meters in this case),
• $g$ is the acceleration due to gravity (approximately 9.8 m/s²), and
• $t$ is the time of flight.

Rearranging the formula for vertical displacement, we have:

$t=\sqrt{\frac{2h}{g}}$.

Substituting the given values into this equation, we find:

$t=\sqrt{<span\; class="vlist-t\; vl}$