A ball is kicked with an initial velocity of 16 m/s in the horizontal direction and 12 m/s in th

A ball is kicked with an initial velocity of 16 m/s in the...

Key Concepts

Projectile Motion

Projectile motion describes the motion of an object that is launched into the air and moves under the influence of gravity alone. In this type of motion, the horizontal and vertical components of the object's velocity are treated separately, where the horizontal motion is uniform (constant velocity) and the vertical motion is uniformly accelerated due to gravity, resulting in a parabolic trajectory.

Kinematic Equations

Kinematic equations are formulas used to relate displacement, velocity, acceleration, and time during an object's motion under constant acceleration. These equations enable the calculation of various parameters such as time of flight, maximum height, and impact speed, which are particularly useful in analyzing projectile motion.

Velocity Decomposition

Velocity decomposition involves breaking down an initial velocity vector into its horizontal and vertical components. This is a fundamental step in the analysis of projectile motion, as it allows the independent examination of the motion along each axis, thereby simplifying the problem-solving process for determining parameters like the range, flight duration, and impact speed.

Gravitational Acceleration

Gravitational acceleration is the acceleration due to Earth's gravity, typically approximated as 9.8 m/s². It is the constant acceleration acting on the vertical component of any projectile, causing it to decelerate as it rises, come momentarily to rest at the peak, and then accelerate downward, and is a crucial factor in computing the vertical motion aspects of projectile trajectories.

Transcript

00:01 We're going to assume that the ball is kicked and the change in the displacement in the y direction is zero meters because it's kicked from the ground and then it lands on the ground, which means that here the initial x component of velocity would be equal to the final x component of the velocity.

00:20 And this would be equal to 16 meters per second because there isn't any acceleration in the x direction.

00:27 Now, for the y component, vy initial is equaling 12 meters per second.

00:36 However, vy final would be the equal in magnitude but opposite in direction.

00:42 So because it would now be traveling downwards.

00:46 And so we can say that then for part a, the magnitude of the final velocity would be equal to the square root of, rather 16 meters.

01:01 Per second quantity squared plus negative 12 meters per second quantity squared and this is equaling approximately 20 meters per second so this would be the magnitude with which it hits the ground and we can then say that the time in the air we know that v y final squared is going to equal v y initial squared plus 2g times delta y and in fact, even simpler, we can say vy final equals vy initial plus gt.

01:46 This is even simpler because then we can simply say that time is going to be vy final minus vy initial divided by g.

01:55 And this is equaling negative 12 meters per second minus positive 12 meters per second divided by negative 9 .80 meters per second divided by negative 9 .80 meters per second.

02:06 Squared and so the time in the air would be 4 .08 seconds...

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