Shot Put Record A men's world record for the shot put, 23.12 m , was set by Randy Barnes of the

Shot Put Record A men's world record for the shot put, 23.12...

Key Concepts

Effect of Launch Height

The effect of launch height on projectile motion accounts for the fact that an object may be released from a point above the ground. This additional height influences the time it takes for the object to reach the ground, thereby impacting the overall trajectory and range. Considering launch height is essential for accurately determining parameters such as the initial speed required to achieve a given range.

Decomposition of Velocity

Decomposition of velocity refers to breaking down the initial velocity vector into its horizontal and vertical components using trigonometric functions like sine and cosine. This is crucial in projectile motion because the horizontal and vertical motions are independent; the horizontal motion occurs at a constant velocity while the vertical motion is influenced by gravity.

Trigonometric Functions in Kinematics

Trigonometric functions, specifically sine and cosine, are used in kinematics to resolve the initial velocity vector into its vertical and horizontal components. These functions allow for the proper application of kinematic equations, providing a systematic way to incorporate the launch angle into calculations that predict the motion behavior of projectiles.

Projectile Motion

Projectile motion describes the trajectory of an object launched into the air and subject only to the acceleration due to gravity. This concept helps in understanding how objects travel through space, including how both horizontal and vertical components of motion coexist and evolve over time. It provides the foundational framework for solving problems where an object is thrown or propelled, such as a shot put, determining how its initial speed and angle affect the distance traveled.

Kinematic Equations

Kinematic equations are a set of mathematical formulas that describe the motion of objects under constant acceleration, such as gravity. They are used to relate displacement, initial velocity, time, and acceleration, making them essential in analyzing the motion of projectiles. These equations enable one to calculate key parameters like time of flight, maximum height, and range in projectile motion problems.

Transcript

00:01 Question 76 states that a men's world record for the shot put, 23 .12 meters, was set by randy barnes of the united states on may 20th, 1990.

00:13 If the shot was launched from six feet above the ground at an initial angle of 42 degrees, what is its initial speed? all right, so we have a shot putter that launches it at a distance i called the y of six feet off the ground, but i converted to 1 .83 meters, because that's what we have.

00:32 We'd like to see.

00:33 It's launched, you know, the horizontal distance, dx is 23 meters.

00:42 We're looking to see what that initial launch speed was of v -0.

00:46 If it's launched, assumingly at some angle, well, not assumingly, sorry, tells us 42 degrees.

00:54 Yeah, what is v -0? okay, so we're told, again, all these terms, dx, d, d, y, and theta.

01:02 So what else may not be obvious to start.

01:04 I'm just going to pick one of the equations that has all of these variables.

01:08 So i'm going to start with my dx equation.

01:11 So my dx, i know that's related to my initial velocity by, you know, v0 times t.

01:20 Well, okay, well, how can this help me? well, i can say, okay, so that's my initial velocity.

01:25 If i took my angle here, if this is theta and this is v0, then my horizontal component or the x direction, which, hey, i should label my x direction, what that means.

01:39 That would be correspond to the cosine of my v0, so that's v0, cosine theta times time and now i'm stuck right i don't know v not i don't know time but i need to solve for v not so i need to keep that term there so perhaps if i first i'll look at my dy equation if i look at this i see okay if i can replace my t term with with what i can get for my x term equation i can eliminate time as a variable and only have v not as my unknown variable so i'm going to do that and note for with my d -y equation, i recognize that my distance in the y direction is negative because i'm going from a higher height to a lower height.

02:33 And of course, the acceleration due to gravity is zero, or is negative as well, not zero.

02:37 And our initial launch speed will have a positive y value.

02:41 So that's why my negatives are real on those two terms.

02:44 And of course, is a t -square at the end here.

02:47 So like i said, in this equation, i'm going to solve for time so i can eliminate that unknown variable and only have b -0 as my unknown.

02:55 So that's my plan here.

02:57 So v .0 cosine theta.

03:01 I can now substitute that into my d .y equation.

03:08 So if i have negative dy, my initial velocity in the y direction is simply v0...