The path of a projectile that is launched h feet above the ground with an initial velocity of t\) feet per second and at an angle 0 with the horizontal is given by the parametric equations
where t is the time, in seconds, after the projectile was launched. The parametric equation for x gives the projectile’s horizontal distance, in feet. The parametric equation for y gives the projectile’s| height, in feet. Use these parametric equations to solve Exercises 69 -70.
The figure shows the path for a baseball that was hit with an initial velocity of 150 feet per second at an angle of 35° to the horizontal. The ball was hit at a height of 3 feet off the ground.
a. Find the parametric equations that describe the position of the ball as a function of time.
b. Describe the ball's position after 1, 2, and 3 seconds. Round to the nearest tenth of a foot. Locate your solutions on the plane curve.
c. How long is the ball in flight? (Round to the nearest tenth of a second. ) What is the total horizontal distance that it travels, to the nearest tenth of a foot, before it lands? Is your answer consistent with the figure shown?
d. Use the graph to describe something about the path of the baseball that might be of interest to the player who hit the ball. Then verify your observation algebraically.
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
Algebra & Trigonometry With Additional Material From College Algebra Essentials (custom Edition For Tidewater Community College)
- Object A is travelling along a circle of radius 2, and Object B is travelling along a circle of radius 5. The object have the same angular speed. Do the objects have the same linear speed? If not, which object has the greater linear speed?arrow_forwardDetermine an equation for the sinusoidal function shown: v (4в/3, 2) (14x/3, 2) (5z/3, 4)arrow_forwardGiven the parametric equations: x =t, y=(t + 1) a) Find the slope at t = 2 b) Find the time t when the particle reaches the point (1, 0). Then, find the equation of tangent line at that particular time.arrow_forward
- A projectile is given an initial velocity of 31.5 m/s at an angle of 51.5 degrees with respect to the horizontal. How far has it moved in the x-direction at the time when its speed in the y-direction is 10.5 m/s? A projectile is launched with an initial velocity of 27.2 m/s at 64.7 degrees with respect to the horizontal. What is the speed of the projectile 1.83 s after being launched. Assume the speed is measured in m/s. A projectile is launched with an initial velocity of 46.8 m/s at an angle of 31.2 degrees with respect to the horizontal. In meters, what is the maximum upward displacement of the projectile?arrow_forwardUse the parametric equations x= sec(t) , y=tan(t), for -pi/2 < t < pi/2. Sketch the curve represented by the parametric equations (include the orientation of the curve) and write the corresponding rectangular equation by eliminating the parameter and Find the equation of the tangent line to the curve at t = pi/4arrow_forwardThe curve r = VI + sin20,arrow_forward
- A particle moves to the left of the parabola. r=4/(1+cos theta) with constant speed of 4 ft/s. when theta=pie/2 Determine the radial component of the velocity and transverse component velocity.arrow_forwardConsider the curve defined by the parametric equations X = cos t, y = 3sec t on the interval 0sts"/2, Eliminate the parameter, t, to find a Cartesian equation for this curve. Use the equation editor to enter your answer in correct mathematical form.arrow_forwardfind parametric equation (cartesian) for tagent line to r=cos(2theta) at theta=2arrow_forward
- A very tall light standard is swaying in an east-west direction in a strong wind. An observer notes that the time difference between the vertical position and the furthest point of sway was 2 seconds. The pole is 40 metres tall. At the furthest point of sway, the tip of the pole is 1° out of the vertical position when measured from the bottom of the pole. Create a sinusoidal equation that models the motion of the tip of the pole as a displacement from the vertical position as a sinusoidal function of time. Assume time starts when the tip of the pole is furthest east. Include a sketch of the graph of your equation. (4 marks)arrow_forwardfind the parametric equations for the line segment from (-2,5) to (7,-1) your equation for x should not be x=t. define your interval for the parameter t.arrow_forwardWrite parametric equations to describe the curves traced by the following motions:arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning