PDM 2.B - Parametric Equations

Given the set of parametric equations:

x(t) = 2t - 1

y(t) = 2t² + 1

Find the ordered pair corresponding to t = 1

Given the parametric equations in radians:

x(θ) = θ + π/2

y(θ) = cos(θ) - 1

Find the coordinate point corresponding to θ = π

Given the parametric equations:

x(t) = e^t - e^-t

y(t) = e^t + e^-t

0 ≤ t ≤ 5

Find the point corresponding with t = 0

Given the set of parametric equations:

x(t) = 2t - 1

y(t) = 2t² + 1

Find the ordered pair corresponding to t = 3

Given the parametric equations in radians:

x(θ) = θ + π/2

y(θ) = cos(θ) - 1

Find the coordinate point corresponding to t = -π

Given the parametric equations:

x(t) = e^t - e^-t

y(t) = e^t + e^-t

0 ≤ t ≤ 5

Find the point corresponding with t = 1

Suppose that a ball is thrown with an initial horizontal velocity of 25 ft/sec and an initial vertical velocity of 15 ft/sec. Assume that the only force acting on the object is due to gravity. Let t = time in seconds since the ball was thrown. Find the parametric equations for the path of the ball. Assume that the starting point is the origin.

Suppose that a ball is thrown with an initial horizontal velocity of 25 ft/sec and an initial vertical velocity of 15 ft/sec. Assume that the only force acting on the object is due to gravity. Let t = time in seconds since the ball was thrown.

x(t) = 25t; y(t) = -16t² + 15t

Graph the parametric equations and find the coordinate point corresponding to t = 1

Suppose that a ball is thrown with an initial horizontal velocity of 25 ft/sec and an initial vertical velocity of 15 ft/sec. Assume that the only force acting on the object is due to gravity. Let t = time in seconds since the ball was thrown.

x(t) = 25t; y(t) = -16t² + 15t

Graph the parametric equations and find the coordinate point corresponding to t = 0.5

Suppose that a ball is thrown with an initial horizontal velocity of 25 ft/sec and an initial vertical velocity of 15 ft/sec. Assume that the only force acting on the object is due to gravity. Let t = time in seconds since the ball was thrown.

x(t) = 25t; y(t) = -16t² + 15t

At what t-value does the maximum height occur?