💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

MMH After leaving the end of a ski ramp, a ski jumper lands downhill at a point that is displaced 51.0 m horizontally from the end of the ramp. His velocity, just before landing, is 23.0 m/s and points in a diretion 43.0-below the horizontal. Neglecting air resistance and any lift he experiences while airborne, find his initial velocity (magnitude and direction) when he left the end of the ramp. Express the direction as an angle relative to the horizontal.

$\left|v_{0}\right|=\sqrt{14.025^{2}+16.82^{2}}=21.90,$ with direction$\tan ^{-1} \frac{14.025}{16.82}=39.82^{\circ}$ to the horizontal

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

University of Sheffield

Lectures

04:16

In mathematics, a proof is…

04:48

In mathematics, algebra is…

03:07

A skier leaves the ramp of…

03:25

01:27

It is observed that the sk…

01:15

08:48

A skilled skier knows to j…

02:04

A 60 kg skier leaves the e…

06:38

A $\mathrm 60 \mathrm{kg}$…

05:11

$\bullet$ $\bullet$ Ski ju…

04:38

A ski jumper starts from r…

09:56

A 62 -kg skier starts from…

03:49

Assume that the skier left…

0:00

A ski jumper starts with a…

01:29

A skier is gliding along a…

03:39

An acrobat on skis starts …

05:58

A skier with a mass of $63…

12:33

A 55-kg skier starts from …

03:05

A man with a mass of $65 \…

09:59

A snow-covered ski slope m…

03:34

From the edge of a cliff, …

01:13

A daredevil on a motorcycl…

So the question states that a skier jumps off a ramp at some unknown speed and angle, and he travels 51 meters and right before he hits the ground, his velocity is 23 meters per second and angle of 43 degrees below the horse on. And our task is to find what this, uh, what his speed is when he goes off the ramp as well as the ankle, he gives off the right. So the first thing we can do is separate his final velocity into components. So to do this mean retry it have an X component and a, uh why component. And then his total velocity looks like this. You be some why and this will be a piece of X and then his. The angle here is 43 degrees. So we know that the co sign of 43 degrees is equal to adjacent over iPod news. So visa vex over the iPod news, which is 23 meters per second. So this means visa backs will be equal to co sign. Sorry, not co sign will be equal to 23 times co sign of 43 degrees and the same thing goes for Visa Boy, except instead of co sign it will be signed. So it'll be 23 times signed of 43 degrees. And so another We know this. We can try and figure out how long, uh, skier is in the air. Four. Um, And to do this, we can use our cinematic equation, which states that the initial velocity in the X direction times the time is equal to e total displacement in the X direction. We know for effect that the initial velocity in the X direction is going to be equal to the final velocity in the X direction because it's projectile motion. So there's no acceleration at all in the horizontal direction. So this component is going to be equal to 23 times co sign of 43 degrees and we can use this in our equation here. So when we plug in what we know, plug in 23 times co sign of 43 degrees. We don't know what the time is, and we know the range he travels is 51 meters. So when we sell for tea, we find that T is approximately approximately equal to put three point 03 seconds and now that we know the time, we can figure out what what his initial velocity here is in the vertical direction. So to do this we can use our other Kitimat equation, which states that the final velocity in the vertical direction is equal to the initial velocity in the vertical direction, plus the acceleration times the time. So we know the final velocity in the vertical direction is going to be negative 23 times sign of 34 degrees. And it's negative because it's pointing downward. The vector is pointing in the downward direction which we're calling negative is equal to the initial velocity which we're trying to find in the Y direction, plus the acceleration which is negative 9.8 meters per second squared times the time, which is 3.3 seconds. And when we solve this for visa wine, we get these. Why is equal to 14 0.1 meters per second. So now that we know what our vertical component is and our horizontal component is, we can so for our capital v up here. So to do this, we know that to find the magnitude of back here. It's the square root of the horizontal component of the velocity, plus the vertical component of velocity squared. Both of these air squared and so we can plug in our our ah vertical component as well. A czar horizontal component, which is 23 co signed 43 degrees. And when we do this, we find that the total magnitude of the velocity is equal to 21 0.90 meters per second. Now, if we want to find what the angle here is a data, we can just take the tan in verse, which is going to be opposite over adjacent, so the opposite is going to be RV. So why and Ari Jason's Bisa vexed where the supply once again is 14 points? Year one and piece of X is 23 cho sun 43 degrees and that will give us our data. And when we played that in and and calculated, we get at the angle is equal to 39.8 degrees, and that is the final answer

View More Answers From This Book

Find Another Textbook

In mathematics, a proof is a sequence of statements given to explain how a c…

In mathematics, algebra is one of the broad parts of mathematics, together w…

A skier leaves the ramp of a ski jump with a velocity of $10.0 \mathrm{m} / …

It is observed that the skier leaves the ramp $A$ at an angle $\theta_{A}=25…

A skilled skier knows to jump upward before reaching a downward slope. Consi…

A 60 kg skier leaves the end of a ski-jump ramp with a velocity of 24 $\math…

A $\mathrm 60 \mathrm{kg}$ skier starts from rest at height $H=20 \mathrm{m}…

$\bullet$ $\bullet$ Ski jump ramp. You are designing a ski jump ramp for…

A ski jumper starts from rest 50.0 $\mathrm{m}$ above the ground on a fricti…

A 62 -kg skier starts from rest at the top of a ski jump, point $A$ in Fig. …

Assume that the skier left the ramp moving horizontally. Treat the skier as …

A ski jumper starts with a horizontal take-off velocity of $25 \mathrm{m} / …

A skier is gliding along at $3.0 \mathrm{m} / \mathrm{s}$ on horizontal, fri…

An acrobat on skis starts from rest $50.0 \mathrm{m}$ above the ground on a …

A skier with a mass of $63 \mathrm{kg}$ starts from rest and skis down an ic…

A 55-kg skier starts from rest at the top of a ski jump, point A in Fig. 6-4…

A man with a mass of $65 \mathrm{kg}$ skis down a frictionless hill that is …

A snow-covered ski slope makes an angle of 35.0° with the horizontal. When a…

From the edge of a cliff, a 0.55 $\mathrm{kg}$ projectile is launched with a…

A daredevil on a motorcycle leaves the end of a ramp with a speed of 35.0 $\…

05:00

ssm The mass of a robot is 5450 $\mathrm{kg}$ . This robot weighs 3620 $\mat…

02:09

The weight of an object is the same on two different planets. The mass of pl…

15:10

ssm A 5.00 -kg ball, moving to the right at a velocity of $+2.00 \mathrm{m} …

03:06

A computer is reading data from a rotating CD-ROM. At a point that is 0.030 …

03:22

Multiple-Concept Example 7 reviews the concepts that play a role in this pro…

03:56

The drawing shows a jet engine suspended beneath the wing of an airplane. Th…

00:31

During a tug-of-war, team A pulls on team B by applying a force of 1100 N to…

02:13

A satellite circles the earth in an orbit whose radius is twice the earth&#x…

04:32

A model rocket blasts off from the ground, rising straight upward with a con…

02:07

At some airports there are speed ramps to help passengers get from one place…