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- 1. Multiple Choice
Given the set of parametric equations:
x(t) = 2t - 1
y(t) = 2t2 + 1
Find the ordered pair corresponding to t = 1
(1, 3)
(1, 5)
(3, 1)
(5, 1)
- 2. Multiple Choice
Given the parametric equations in radians:
x(θ) = θ + π/2
y(θ) = cos(θ) - 1
Find the coordinate point corresponding to θ = π
(3π/2, -2)
(-1, 3π/2)
(π/2, -1)
(-1, π/2)
- 3. Multiple Choice
Given the parametric equations:
x(t) = et - e-t
y(t) = et + e-t
0 ≤ t ≤ 5
Find the point corresponding with t = 0
(0, 2)
(0, 0)
(7.25, 7.52)
(-1, 0)
- 4. Multiple Choice
Given the set of parametric equations:
x(t) = 2t - 1
y(t) = 2t2 + 1
Find the ordered pair corresponding to t = 3
(5, 37)
(3, 19)
(3, 37)
(5, 19)
- 5. Multiple Choice
Given the parametric equations in radians:
x(θ) = θ + π/2
y(θ) = cos(θ) - 1
Find the coordinate point corresponding to t = -π
(-π/2, -1)
(-1, -π/2)
(π/2, -1)
(-1, π/2)
- 6. Multiple Choice
Given the parametric equations:
x(t) = et - e-t
y(t) = et + e-t
0 ≤ t ≤ 5
Find the point corresponding with t = 1
(0, 0)
(2.35, 3.08)
(7.25, 7.52)
(-1, 0)
- 7. Multiple Choice
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.
x(t) = 25t; y(t) = -.5t2 + 15t
x(t) = 25t; y(t) = -16t2 + 15t
x(t) = 15t; y(t) = -16t2 + 25t
x(t) = 15t; y(t) = -.5t2 + 25t
- 8. Multiple Choice
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
(25, -1)
(25, -241)
(25, 0)
(25, 1)
- 9. Multiple Choice
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
(12.5, 3.5)
(12.5, 7.5)
(12.5, 1)
(12.5, 10.2)
- 10. Multiple Choice
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?
t = .5
t = .46875
t = 0.25
t = .9375
- 11. Multiple Choice
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
What is the maximum height of the object?
3.5 ft
3.52 ft
2.75 ft
0 ft
- 12. Multiple Choice
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
After how many seconds will the object hit the ground?
0.5 seconds
0.46875 seconds
1 second
.9375 seconds
- 13. Multiple Choice
An object is thrown from a height of 5 meters with a horizontal velocity of 10 m/sec and a vertical velocity of 8 m/sec. Assume that the only force acting on the object is gravity. Find the parametric equations for the path of the ball:
x(t) = 10t; y(t) = -.5t2 + 8t + 5
x(t) = 10t; y(t) = -4.9t2 + 8t + 5
x(t) = 10t + 5; y(t) = -4.9t2 + 8t
x(t) = 8t + 5; y(t) = -4.9t2 + 10t
- 14. Multiple Choice
An object is thrown from a height of 5 meters with a horizontal velocity of 10 m/sec and a vertical velocity of 8 m/sec. Assume that the only force acting on the object is gravity. This can be modeled using:
x(t) = 10t; y(t) = -4.9t2 + 8t + 5
At what time does the object reach its maximum height?
.82 seconds
1 second
1.64 seconds
.75 seconds
- 15. Multiple Choice
An object is thrown from a height of 5 meters with a horizontal velocity of 10 m/sec and a vertical velocity of 8 m/sec. Assume that the only force acting on the object is gravity. This can be modeled using:
x(t) = 10t; y(t) = -4.9t2 + 8t + 5
What is the maximum height?
8.27 meters
8.1 meters
10.3 meters
8.25 meters
- 16. Multiple Choice
An object is thrown from a height of 5 meters with a horizontal velocity of 10 m/sec and a vertical velocity of 8 m/sec. Assume that the only force acting on the object is gravity. This can be modeled using:
x(t) = 10t; y(t) = -4.9t2 + 8t + 5
After how many seconds does the object hit the ground?
.48 seconds
.96 seconds
2.11 seconds
.82 seconds
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