A soccer player kicks a rock horizontally off a cliff 40.0...

Key Concepts

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and is subject only to the acceleration due to gravity. This concept involves breaking the motion into horizontal and vertical components that act independently, with the horizontal motion having constant velocity and the vertical motion experiencing constant acceleration.

Free-Fall Kinematics

Free-fall kinematics involves the equations that describe the motion of an object under the influence of gravity, neglecting air resistance. This concept is crucial for determining how long an object takes to fall a certain vertical distance and for calculating other parameters of motion when the only acceleration is due to gravity.

Sound Propagation

Sound propagation is the study of how sound waves travel through a medium, typically at a constant speed in air under normal conditions. This concept is used to determine the time it takes for sound generated by an event to reach a listener, allowing for the separation of time between the event occurring and being heard.

Separation of Time Intervals

The separation of time intervals involves breaking the total elapsed time into distinct parts corresponding to different processes. In problems combining multiple phenomena, such as a falling object and the subsequent sound reaching an observer, this concept is key to setting up and solving equations that correlate the different time components.

Transcript

0:00 Hello.

00:02 In this problem, we have a soccer player that is a standing of a cliff and he shot a rock horizontally with unknown speed and this rock hit a pool of water after three seconds.

00:21 He started to hear the splash.

00:23 So he heard the splash of the rock hitting the pool three seconds after he kicked the ball itself.

00:29 The height of the cliff is 40 meters and now we are asked to determine the initial velocity that the ball was kicked with.

00:39 So we have theta initial is equal to zero because it's fired horizontally and the height of the cliff is 40 meters.

00:49 And we have the time, total time, which is three seconds.

00:56 We also have the velocity of sound which is 343 meters.

01:00 In this problem.

01:04 Okay, so now we know that this time here consists of two parts.

01:09 The time of the trip, the time it takes for the rock to hit the pool, and then the time the sound takes to return back to the ear of the player.

01:21 Here, we will neglect the height of the player himself, and we will assume that the sound will reach the same point that the ball was kicked from.

01:31 And of course sound travels in straight lines or spherical waves to be accurate, but here, this straight line here represent the distance that the sounds cross when leaving the pool until it reaches the ear of the player.

01:48 So first, let's use the givens we have to determine the time of the trip itself, i .e.

01:57 The time that it takes for the rock to reach the swimming pool.

02:01 So from kinematics, we know that y is equal to the v iy, the initial velocity in the y direction, multiplied by time, minus half g, t square.

02:15 In this problem, because the ball was kicked horizontally, so the initial velocity in the y direction is zero.

02:23 So this part is zero.

02:25 And now we can say that y here is equal to negative 40 and this is equal to half multiplied by 4 .8 t squared.

02:39 From here, t squared is equal to 40 divided by 4 .9 and taking the square root, we have t is equal to 20 over 7, which is approximately 2 .857 seconds.

03:00 So this is here, the time of the trip...

Please give Ace some feedback