An astronaut laying down shoots a golf ball from a slingshot. The golf ball has an initial velocity of 5.5m/s at an angle of 22.0 degrees just above the newly discovered planet's surface. The ball hits the planet 14m away from where it was launched, being launched and hitting the planet at roughly the same height. You will find ● 1. The amount of time the golf ball stays in the air The acceleration due to gravity on this planet Draw a diagram of the path of the golf ball, labeling all given variables in your diagram. 2. Draw the directions of the initial velocity and gravitational acceleration, and displacement vectors. 3. Take the three vectors from the previous problem and form them into a right triangle, changing the velocity vector into a displacement type of vector by multiplying the velocity by t and doing similarly with your acceleration vector by multiplying it by ½ t². Also label the 22.0 degree angle in your triangle. 4. Find an expression for cosine using this triangle. 5. Solve your cosine expression for time, plug in the values for your variables, and get an answer 6. Find an expression for the sine of your triangle (use the same triangle as before). 7. Solve your sine expression for your acceleration, and plug in time (from your answer to #5) and your other given variables.
An astronaut laying down shoots a golf ball from a slingshot. The golf ball has an initial velocity of 5.5m/s at an angle of 22.0 degrees just above the newly discovered planet's surface. The ball hits the planet 14m away from where it was launched, being launched and hitting the planet at roughly the same height. You will find ● 1. The amount of time the golf ball stays in the air The acceleration due to gravity on this planet Draw a diagram of the path of the golf ball, labeling all given variables in your diagram. 2. Draw the directions of the initial velocity and gravitational acceleration, and displacement vectors. 3. Take the three vectors from the previous problem and form them into a right triangle, changing the velocity vector into a displacement type of vector by multiplying the velocity by t and doing similarly with your acceleration vector by multiplying it by ½ t². Also label the 22.0 degree angle in your triangle. 4. Find an expression for cosine using this triangle. 5. Solve your cosine expression for time, plug in the values for your variables, and get an answer 6. Find an expression for the sine of your triangle (use the same triangle as before). 7. Solve your sine expression for your acceleration, and plug in time (from your answer to #5) and your other given variables.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
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Transcribed Image Text:A:
Consider the kinematic problem that follows, and then follow the steps below to solve the problem
using vectors rather than plugging into kinematic equations.
An astronaut laying down shoots a golf ball from a slingshot. The golf ball has an initial velocity of
5.5m/s at an angle of 22.0 degrees just above the newly discovered planet's surface. The ball hits the
planet 14m away from where it was launched, being launched and hitting the planet at roughly the
same height.
You will find
The amount of time the golf ball stays in the air
● The acceleration due to gravity on this planet
●
1. Draw a diagram of the path of the golf ball, labeling all given variables in your diagram.
2. Draw the directions of the initial velocity and gravitational acceleration, and displacement
vectors.
3. Take the three vectors from the previous problem and form them into a right triangle, changing
the velocity vector into a displacement type of vector by multiplying the velocity by t and doing
similarly with your acceleration vector by multiplying it by ½ t². Also label the 22.0 degree angle
in your triangle.
4. Find an expression for cosine using this triangle.
5. Solve your cosine expression for time, plug in the values for your variables, and get an answer
6. Find an expression for the sine of your triangle (use the same triangle as before).
7. Solve your sine expression for your acceleration, and plug in time (from your answer to #5) and
your other given variables.
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