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MMH A golfer, standing on a fairway, hits a shot to a green that is elevated 5.50 m above the point where she is standing. If the ball leaves her club with a velocity of 46.0 m/s at an angle of 35.0 above the ground, find the time that the ball is in the air before it hits the green.

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Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Rutgers, The State University of New Jersey

Simon Fraser University

University of Winnipeg

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

10:12

A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

01:33

A golfer, standing on a fa…

02:09

04:59

Before starting this probl…

02:40

04:48

A golfer hits a shot to a …

03:37

05:08

A golfer tees off from the…

04:05

01:32

IP A golfer tees off on le…

26:08

A professional golfer hits…

Suppose that the golf ball…

04:45

MMH A golfer imparts a spe…

02:53

A golfer hits a shot to an…

So the question states that a Oh, it's hit at 46 meters per second, an angle of 35 degrees and it hits the green. That's Ah, 5.5 meters, um, elevated at 5.5 meters. And so we're trying to find at what time the ball hits the green. So to do this, we're gonna have Teoh usar kim attics Where Notice to you. Ah, solved for the time. And when we do this, we're probably gonna get two different routes. One route where it first passes this 5.5 meter mark and another when it first touches this 5.5 meter mark. So we have to pick the correct one. Um, so equation, we need to use states that the change in the displacement is equal to the initial velocity times the time plus 1/2 times the acceleration tons of times square. So for this case, we really just need to focus on the vertical velocity, um, the vertical component of the velocity. So to figure out what this V supply is, we can say that thesis I nine of 35 degrees is he good to opposite over iPod news, which is Visa by over 46 which means Visa Y is equal to 46 times sign of 35 degrees. So now that we know this, we completed into the equation, we have appear. So we know that the displacement is going to be 5.5 meters because it's going to land on top of the green. We know that the initial velocity in the vertical direction is 46 signed 35 degrees. We're trying to find what tea is. Um, we know that the acceleration due to gravity is negative, 9.8 meters per second squared, and we have this extra t here. So when we simplify, this will get an equation such as this, so it'll be negative. 4.9 t square plus 26 point three a t minus 5.5 is equal to zero. So there's two things you can do here to sell for two. You can either use quadratic formula, which states that, um, the roots are equal to the opposite. Opposite B plus or minus square root B squared minus four a. C over two A. Where this is your a term. This is your be term and this is your C term, and that will give you two different routes and this kind of a little bit difficult if you don't have a calculator. But the easier way to do this would be just to graph this equation here and look at where it crosses the X axis. So that's what I did. If you look here, this is our equation and the two routes that we have our point to 17 and 5.166 So we know that we're gonna get to roots. And we know for a fact that this route, this first route is not not the route we need to choose, because this is the point where the ball first passes 5.5 meters. So this is incorrect route. The correct word we need to choose is 5.166 seconds. So our answer for the time that it takes to reach this point here is five 0.166 seconds

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