If an object is thrown on the moon, then the parametric equations of flight are x(t)...
If an object is thrown with a velocity of v feet per second at an angle of θ with the horizontal, then its flight can be modeled by, x = (v cos θ ) t and y = v (sin θ ) t - 16 t2 + h where t is in seconds and h is the object's initial height in feet above the ground. x is the horizontal position and y is the vertical position, and - 16 t2...
An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall, and the initial velocity of the ball is 50 ft per sec. The height s of the ball in feet is given by the equation s=-2.7 t²+50 t+6.5, where t is the number of seconds after the ball was thrown. Complete parts a and b.a. After how many seconds is the ball 14 ft above the moon's surface?After _______ seconds the ball will...
In 1971 Alan Shepard and Ed Mitchell spent 33 hours on the Moon as crew members of Apollo 14. Shepard, one of the original Mercury astronauts, was 47 years old and is the oldest man to walk on the lunar surface. While on the Moon, Shepard hit two golf balls using an improvised golf club. After striking the second ball, Shepard said “miles and miles and miles”, a reference to the distance the ball travelled. Owing to the lack of...
An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall, and the initial velocity of the ball is 50 ft per sec. The height s of the ball in feet is given by the equation s =-27t2 + 50t+ 6.5, where t is the number of seconds after the ball was thrown. Complete parts a and b. a. After how many seconds is the ball 18 ft above the moon's surface?
using parametric equations
and ange 6. Chris and Linda are standing 78 feet apart. At the same time, they each throw a softball toward each other. her ball with an initial velocity of 45 ft per second with an angle of inelination of 44. Chris throws her ball with an initial velocity of 41 feet per second with an angle of inclination of 39 a. Find two sets of parametric equations that represent a model of the problem situation. b....
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8.8.47 A rocket is launched from the top of an 8-ft platform. Its initial velocity is 144 ft per sec. It is launched at an angle of 60 with respect to the ground, (a) Find the rectangular equation that models its path. What type of path does the rocket follow? (b) Determine the total flight time and the horizontal distance the rocket travels. (a) Using y to indicate the height of the rocket and x to...
18) A ball is thrown across a playing field from a height of 5 ft above the ground at an angle of 45° to the horizontalat a speed of 20 ft/s. It can be deduced fromphysical principles thatthe path of the ball is modeled by the function f(x) = - 32 x +x+5 400 a. At what horizontal distance xis the ball 7 ft high? b. At what horizontal distance x does the ball hit the ground?
6) A ball is thrown across a playing field fror Toss a playing field from a height of 4 ft above the ground at an angle of 45 to the horizontal at a speed of 20 fus. It can be deduced physical principles that the path of the ball is modeled by the function x + x +4 a. At what horizontal distance x is the ball 6 At high? b. Does the ball reach a height of 10 ft?...
2. A baseball thrown from the outfield, a golf ball, or a thrown football, all will follow a trajectory (path) that has horizontal as well as vertical displacement components. If we neglect the air friction on the ball, the path will be a perfect parabolic trajectory. The equations for the displacement of the ball are: Take gravity g as 9.81 meters per second, and the initial velocity, Vo, equal to 35 meters/second. Use Excel to show the ball trajectory for...
An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t),sin(t)) . Assume 0 < t < ?/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle in the first quadrant. (Connect the origin with the y-intercept and x-intercept of the tangent line.)