An arrow is shot upward, with an initial velocity of 85 meters per second, at an angle of 31° with respect to the horizontal. The arrow is shot from a height of 6meters above the ground.The horizontal distance x from the starting point and the height y above the ground of the arrow t seconds after it is shot are given by the parametric equationsbelow.3(vo cos e)ty=-4.9f +(vo sin0)t+hX=Here v, is the initial velocity, 0 is the initial angle with respect to the horizontal, and h is the initial height.Use the equations to answer the following questions.(a) When does the arrow reach its maximum height?Do not round any intermediate computations. Round your answer tothe nearest hundredth.seconds(b) What is the maximum height of the arrow?Round your answer to the nearest tenth.| meters

When an object is thrown in air against the gravitational pull, then the motion of object is called…

An arrow is shot upward, with an initial velocity of 85 meters per second, at an angle of 31° with respect to the horizontal. The arrow is shot from a height of 6 meters above the ground. The horizontal distance x from the starting point and the height y above the ground of the arrow t seconds after it is shot are given by the parametric equations below. x=('%, cos®): y=-4.9?+(vo sine)t+h Here vo is the initial velocity, 0 is the initial angle with respect to the horizontal, and h is the initial height. Use the equations to answer the following questions. (a) When does the arrow reach its maximum height? Do not round any intermediate computations. Round your answer to the nearest hundredth. | seconds (b) What is the maximum height of the arrow? Round your answer to the nearest tenth. meters

An arrow is shot upward, with an initial velocity of 85 meters per second, at an angle of 31° with respect to the horizontal. The arrow is shot from a height of 6 meters above the ground. The horizontal distance x from the starting point and the height y above the ground of the arrow t seconds after it is shot are given by the parametric equations below. x=('%, cos®): y=-4.9?+(vo sine)t+h Here vo is the initial velocity, 0 is the initial angle with respect to the horizontal, and h is the initial height. Use the equations to answer the following questions. (a) When does the arrow reach its maximum height? Do not round any intermediate computations. Round your answer to the nearest hundredth. | seconds (b) What is the maximum height of the arrow? Round your answer to the nearest tenth. meters

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 53E

See similar textbooks

Similar questions

Epicycloid If the circle C of Exercise 63 rolls on the outside of the larger circle, the curve traced out by P is called an epicycloid. Find parametric equations for the epicycloid. Hypocycloid A circle C of radius b rolls on the inside of a larger circle of radius a centered at the origin. Let P be a fixed point on the smaller circle, with the initial position at the point (a,0) as shown in the figure. The curve traced out by P is called a hypocycloid. a Show that parametric equations of hypocycloid are x=(ab)cos+bcos(abb) y=(ab)sinbsin(abb) b If a=4b, the hypocycloid is called an asteroid. Show that in this case parametric equations can be reduced to x=acos3y=asin3 Sketch the curve. Eliminate the parameter to obtain an equation for the asteroid in rectangular coordinates.
Longbow CurveIn the following figure, the circle of radius a is stationary, and for every , the point P is the midpoint of the segment QR. The curve traced out by P for 0<< is called the longbow curve. Find the parametric equations for this curve.
Shooting into the Wind Suppose that a projectile is fired into a headwind that pushes it back so as to reduce its horizontal speed by a constant amount . Find parametric equations for the path of the projectile.
Gear Trains Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n1 and the second gear has n2 teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If 1 and 2 are the angular velocities of the first and second gears, respectively, then v2=v1r22=r112=r1r212=n1n21 The first gear in a single-stage gear train has 42 teeth and an angular velocity of 2 revolutions per second. The second gear has 7 teeth. Find the angular velocity of the second gear.
Gear Trains Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n1 and the second gear has n2 teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If 1 and 2 are the angular velocities of the first and second gears, respectively, then v2=v1r22=r112=r1r212=n1n21 The second gear in a single-stage gear train has 6 teeth and an angular velocity of 90 revolutions per minute. The first gear has 54 teeth. Find the angular velocity of the first gear.
A baseball is hit at a point 3 feet above the ground toward the left field fence. The fence is 10 feet high and 375 feet from home plate. The path of the baseball can be modeled by the parametric equations x=115cost and y=3+115sint16t2. Does the baseball go over the fence when it is hit at an angle of =30 ? Does the baseball go over the fence when =35 ?